What if Hitler won the war? What if the South triumphed at Gettysburg? What if things went a bit wrong in October 1962? What if superheroes were real, and the Cold War got worse? What if I turned left instead of right at the traffic lights? It's almost a human compulsion to ask what might have happened if events in the past had happened differently, and what the resulting world would look like. Would it be Heaven on Earth or a fascist nightmare? So as much as we like to imagine them, we like to read and write them as well. As a genre, however, Alternate History is amazingly fluid, so you'll want to check out Write A Story for basic advice that holds across all genres. You'll also want to decide what specific genre you want to focus on and be familiar with that as well. Take note also that what we're discussing here is writing an Alternate History as an independent genre, not so much an Alternate Universe inside a pre-existing show or format (such as 'What if Kirk had never been made captain of the Enterprise?' or 'What if the Doctor had never left Gallifrey?') - however, the two are quite similar, so if you're intending to write one of these you may nevertheless find something of interest and use here.
Necessary TropesWhat If? is essential to this genre. It's the fundamental question that you're asking in the text; what if this happened differently? For Want of a Nail is also quite important; we seem to enjoy imagining that drastic, world-spanning changes in history can result from tiny, seemingly insignificant events; as the poem that forms the title goes, an entire kingdom falls because a horseshoe isn't nailed in properly. It allows the reader to imagine that no matter how small their actions seem, they ultimately make a difference in determining how history is formed. Conversely, In Spite of a Nail is also quite important; it's often easier for writers and readers to imagine how differently the world might have gone if they're able to see something that's familiar to them slightly altered, despite how unlikely it would be that this element would even exist in the Alternate History. It also enables commentary, satire and parody on the actual world, by framing notable figures, events and locations in different light. For example, The Two Georges features Richard Nixon as a used car salesman in a world where America never gained independence from Great Britain; despite it being very unlikely that Nixon would even have been born in this alternate world, his presence allows the reader to see how different things are and to gain both an insight into and commentary on Nixon himself.
Choices, ChoicesMost importantly, what genre do you intend to write? The most obvious is Science Fiction, as that is how most Alternate Histories are classified in bookstores, but truth be told that is quite misleading; many Alternate Histories may have absolutely nothing in common with Science Fiction at all. In fact, it's perhaps more accurate to refer to an Alternate History as a setting rather than a genre, as practically any story can be told within the boundaries of the Alternate History; a Space Opera, a Detective Murder Mystery, a Romantic Drama, a Historical Novel, and so on. It goes without saying that no matter what genre you pick, you'll need to be familiar with the conventions and principles of that genre in order to effectively write it. You also need to chose what the 'point of divergence' (namely, the point in history where 'our' history and the history of the Alternate World diverge from each other) in your story is, and when / how it occurs. You don't need to actually show the point of divergence if it doesn't relate directly to your story, but you'll still need to have developed a full backstory as to how your Alternate History has developed since the Point in order that you can consistently and accurately present and develop your history in the text, and so that you avoid inconsistencies. As a result, even if your story isn't explicitly a historical novel, you'll still benefit from an understanding of history and how it works (and especially the history of the period that the Point occurs in) in order to be able to construct a convincing alternate world for your reader. Related to the "when" of the point of divergence is the "how." When setting out to write an Alternate History work, one must choose where to put the work on the Sliding Scale of Alternate History Plausibility. Is the point of divergence going to be a mundane, very believable one (for example, the bomb-bay doors on the Enola Gay locked up, causing one of the nukes to not be delivered during World War II, which allows the Japanese leadership to justify fighting and cause a much worse ending to the war) or a more fantastic, less realistic one (known in the usual parlance as an "Alien Space Bats;" for example, an alien race shoots down the Enola Gay with a space laser, preventing the delivery of the bomb and prolonging the war)? It doesn't matter what kind of point of divergence one chooses, but it must be remembered that Alternate History should be about following that point of divergence realistically. The point of divergence can make no sense, but if the repercussions that follow are in line with what such an event would cause in relation to reality, the story is probably on the right track.
PitfallsAs You Know, a clunky-written Alternate History can suffer too much direct and obvious exposition. Alternate History presents a bit of a thorny problem here, as you still need to establish for your reader that the story is set in an alternate history (which can be quite complex and tricky in itself) whilst still allowing them to pick up the pieces for themselves. It is especially important in this genre to Show, Don't Tell; avoid having characters give history lectures to each other in casual conversation or discuss (or even think) things that they'd already know and wouldn't even raise if they weren't considerately thinking of a hypothetical reader who might need to know all this stuff. Try and make it subtle, so that the reader can work out for themselves what's going on based on their understanding of how things did progress in our history rather than having it spelled out for them in crayon; rather than having your characters give a lecture on, say, how Joseph McCarthy was elected to the presidency and what effects this has had in direct conversation, having a character watch a news broadcast which discusses President McCarthy's latest anti-communist initiative will allow the reader to work out for themselves how something is different in a more subtle and interesting fashion. Depending again on the genre, an inaccurate or poor understanding of history can affect how credible your Alternate History is. The fact that it's not the 'real' history is not license for you to slack off on doing your historical research; some things happening differently are a lot more likely and credible than others. Research the historical period you're writing thoroughly; your audience is not stupid, is greatly interested in the historical period you're dealing with and will notice if you didn't check your facts. If you're writing a historical novel about Napoleon triumphing at Waterloo, then having him win through demonstrating superior tactics and the failure of the Allied forces to mount an effective counterattack (which could have happened) will be credible; giving him an atomic bomb which he proceeds to drop on Wellington's forces will have readers throwing your work against the wall with great force—although, granted, it could make for some... unorthodox comedy, if done well. If, however, you're writing a Science Fiction thriller in which time travellers go back in time to give Napoleon an atom bomb, that could work as well. It's also common for writers to have characters speculate on how things might have gone differently in the Alternate History, with their musings almost always resulting in how things actually did progress in our history. Try to avoid this, or play with it; not only is it something of a cliche, but it's also unlikely that they'd figure out exactly how things went in our world. As an example of how to do it right, consider Philip K. Dick's The Man in the High Castle, which is set in a history where the Nazis and Imperial Japan won World War II, centres around a novel that speculates what might have happened if the Allies had won - and in that novel, the progress of World War II is still completely different from how it was really won in our history. If your Alternate History also revolves around a central figure making the change (say, a prominent military general), avoid Mary Sue-ing him or her; someone who makes a different decision that affects all of history is interesting. Someone who has such amazingly perfect insight that allows them to see exactly what will happen if they make a certain decision, which thus allows them to make the 'correct' decision with almost every important decision that they make, wins a war single-handedly and demonstrates repeatedly ad nauseam what an amazingly wonderful person they are... isn't. Particularly since they clearly didn't have perfect 20-20 foresight and always made the right decisions since, you know, they would have if they did. Try to avoid (or at least use with caution) Alternate History Wank, wherein the entire world seems to get taken over by two or three super-empires. While certain nations have managed to create empires which have spanned large amounts of territory and huge populations in Real Life, there is a tendency in Alternate History fiction to over-simplify just how easy, homogeneous and successful these empires manage to be and underestimate the various difficulties they face, such as the logistical headaches of managing an empire that spreads over a huge area of territory and the further headaches of managing the vast, varied population of said area. Furthermore, contrary to what users of this trope would have you believe nothing lasts forever, and even successful empires only tend to last for a finite period of time; even the Mongol Empire, one of the most successful and far-reaching empires ever seen by humanity, didn't manage to last much more than 160 years before eventually falling apart, and certainly didn't even come close to conquering the entire world (or anything near it). While it can be interesting and fun to create new and original empires, you should keep these realities in mind lest your work begin to look like a Mary Sue on a national scale. One further note; in roughly 90% of Alternate Histories, Hitler Wins. The Second World War is a big breeding ground for Alternate Histories, given the fascinatingly brutal and evil nature of the Nazi / Imperial Japanese regimes and how close they actually did come to winning. What this means, however, is that almost every possible idea that can be done around this has been done. If you are going to use World War II as a starting point, try and find something as fresh or new as possible to do with it. Or perhaps choose another, less explored historical period as a starting point; The First World War, for example, is hardly used at all. The American Revolutionary War and the American Civil War also face these concerns, to less extents (and it's interesting to note how so many of them revolve around America's influence on the world, incidentally). Likewise, Alternate Histories where women are in charge? Been done many many many times. Try and find something new to say.
Potential SubversionsAlternate History is itself a subversion of established history; it's showing what didn't happen, but might have. In Spite of a Nail is a prominent subversion; as most Alternate Histories imagine that changes in the historical narrative would result in a drastically different world, it might be fun to imagine how the world might somehow muddle through to be almost exactly the same despite the change. Also, don't just focus on what the 'obvious' alternate outcome might have been; just because Hitler Wins, that doesn't mean that the Thousand Year Reich is just around the corner; supposing he wins the Second World War, but Nazi Germany is later crushed in a Nuclear War with the United States? History is always moving, and things don't always happen the way we think they will. Try for a neglected alternate course of events. For instance, instead of the South winning the Civil War, why not explore a universe where the North won in a Curb-Stomp Battle within the month?
Suggested Themes and AesopsFor Want of a Nail; as discussed above, the idea that small changes result in big effects on the time line is a very popular one. Equally, In Spite of a Nail; it's also popular to imagine that things might be more or less the same despite big changes in history.
Suggested PlotsAgain, this depends largely on the genre you intend to write your Alternate History in. Murder Mysteries and Detective Stories are quite common, though, since they allow the Detective character to enter numerous different areas of society in order to establish exactly how the world is different in this Alternate History than it is in our own. Otherwise, Alternate Histories tend to be Ensemble pieces, with a large cast of characters from a number of different viewpoints that allow the reader to get many different perspectives on how the Alternate World is different from 'our' world. You may also construct a Travelogue in which the plot serves largely to show off the alternate world.
Set Designer / Location ScoutLimited only by your imagination and the genre you intend to choose. However, setting the Alternate History in a very familiar city or locale and then giving it a twist (such as having a character visit the UN Building in London, England) can be quite effective. You may also wish to construct a Parallel World scenario, in which the characters from the real world cross over into the alternate world (or vice versa) in order to establish directly the differences between the two. Of course, the farther away you get from "What if?", the more changes to the physical fabric of the world can be made; using a Steam Punk setting for "What if 9/11 never happened?" would be distracting at the least
Props DepartmentAgain, limited only by the setting of the Alternate History. If you're setting it in a particular historical period, however, make sure the props make sense and are historically appropriate (again, giving Napoleon the atom bomb is a no-no unless you can really sell it).
Costume DesignerSee above. It can be quite effective to have a what was / is a subculture or sub-fashion be considered mainstream in the Alternate History, and vice-versa. It can also be effective to have a historical fashion become popular out of time; in an alternate 2000, we might still be wearing flared trousers...
Casting DirectorIn Spite of a Nail aside, it can be quite effective having historical figures appear in your story in drastically different contexts to demonstrate how the world is different; the aforementioned President Joe McCarthy for example, or used-car-salesman Richard Nixon. Again, make sure that they're accurate and appropriate for the historical setting, and keep in mind what's credible; Roman Emperor Richardus Nixonus is possibly stretching things a bit too far.
Stunt DepartmentAgain, limited only by the genre you're using and what you want to do. Noticing a pattern, here?
Extra CreditAs with any genre you intend to write, read other examples. They'll show you what works and what doesn't. It's interesting to note, though, that Alternate History is almost exclusively a literary genre, with very few examples outside of the written word; this is possibly because establishing an Alternate History, and in particular the background and nuances that led to the development of this alternate world, can be quite complex and difficult to keep straight, and hard to establish within the short time frame of a movie or a television episode. Of particular note here, however, is Harry Turtledove, the 'Master of Alternate History', who writes in this genre almost exclusively. Due to his prolific nature, however, Turtledove straddles both the greats and the epic fails; at his best he's a fine example of what to do well, at his worst, he's a sobering reminder of what can go wrong. Take note of his multi-volume series, however - Worldwar, a sci-fi epic in which aliens invade during World War II and really muck things up, or Timeline-191, a historical series focusing on the Confederacy winning the American Civil War, going through an alternate First World War and alternate Second World War as well; whilst at their best they're compelling reading, he's quite susceptible to As You Know Syndrome as a result of the sheer complexity and length of such works.
The Epic Fails