Face front, True Believers!
'Dashing' Doc Nemesis here! So, you wanna write like Smilin' Stan himself huh? Well, there's a reason they call him The Man - this is the man who co-created the Amazing Spider-Man, the Fantastic Four, the Incredible Hulk, The Uncanny X-Men and, well, a fairly large chunk of what we today know as the Marvel Comics Universe. If you really want to write like Stan, you should check out Write a Story for some general story-telling tips, and Write a Superhero Comic for some genre-specific ideas. Then, pick up that pen, put it to paper, and get that punchy prose pouring!
Necessary TropesStan made his name and did some of his finest work with Superheroes, and that's what he's most known for. But in particular, he's the man who, even if he didn't actually invent it, actually put into words the basic ethos of the typical Super Hero - the idea that With Great Power Comes Great Responsibility, and it is the responsibility of those with power to use it in a way that benefits humanity. His superheroes are defined by this code, his super-villains by their refusal of it.
This isn't to say that his heroes are entirely exemplary, however; a key element of Stan's legacy in superhero comics is that he introduced the world to superheroes who possessed personal problems and were fraught with flaws and failings that were as essential to their character make-up as their super-powers, in direct contrast to the paragons who dominated the genre beforehand. For example, Spider-Man initially used his powers for his own personal benefit, not to fight crime; it was only when his flippant refusal to use his powers to stop a robber indirectly led to the murder of his uncle that he accepted a greater responsibility that his powers came with to try and atone. The trend continues; Iron Man was a flippant, cavalier playboy who struggled with alcoholism, the Fantastic Four a squabbling, dysfunctional family riddled with as much pettiness and bickering as any, the Incredible Hulk essentially the walking personification of uncontrollable anger management problems, and so on. Several of Lee's heroes are also physically disfigured or challenged, which adds a further level of prejudice; as the most prominent examples, Ben 'The Thing' Grimm is a decent-hearted man trapped in the body of a hideous rocky monster, Bruce Banner turns into the hideous, uncontrollable 'Hulk' whenever his anger rages out of control, and Professor Charles Xavier ('Professor X') is a brilliant telepath who is physically confined to a wheelchair.
This applies to villains as well, the best of whom are not mere one-dimensional blackhearts; to take two prominent examples, whilst Dr. Doom is a mad scientist and a tyrant he also possesses a warped-but-strict code of honour which saw him team up with his hated rivals as well as trying to kill them, whilst Magneto, the Knight Templar villain of X-Men, was a Holocaust survivor who feared what had happened to him under the Nazis would happen to his fellow mutants in the present day - in that story's mirroring of the 1960s civil rights struggles he was explicitly intended to parallel Malcolm X, just as Professor X was intended to parallel Martin Luther King. In short, whilst we might not agree or like the villains, we can see where they're coming from.
These personal problems extended to the world the superheroes lived in, which was riddled with All of the Other Reindeer syndrome; not only were his stories set primarily in the Real Life metropolis of New York City (as opposed to the made-up locales that Superman and Batman inhabited), but in his world superheroes were more often as not regarded with suspicion and fear than the awe that previous superheroes had received. Spider-Man was widely mocked and reviled by the public, and the X-Men suffered from Fantastic Racism due to their naturally occurring mutations (which, not uncoincidentally, allowed Lee and his collaborators to examine and parallel the very real racial strife that existed in 1960s America). Even the more publicly 'acceptable' heroes such as the Fantastic Four remained at the mercy of the court of public opinion.
Stan's writing also contains numerous distinctive quirks. Purple Prose is prevalent! Added Alliterative Appeal Abounds! His characters always exchange exclamations! Just look at the names of his characters; Peter Parker! Reed Richards! Susan Storm! Bruce Banner! Matt Murdoch! Scribblin' Stan loved Alliterative Names!
One further note; whilst this trope is named for Stan Lee, it is not for us to forget the equally vital contribution of his artist/co-writer collaborators whom he created the characters with, such as Jack Kirby and Steve Ditko. In fact, you must remember during Lee's finest period was using the "Marvel" or "Plot first" method: Lee would give a basic outline of a story and the artist is responsible as a co-writer for fleshing out the details in the artwork. Afterward, the artwork would be returned to Lee who would write the dialogues and the captions and thought bubbles. In essence, the artist is responsible for the layout, scene breakdowns, visual design and battle choreography. For instance, Lee might have asked for a superhero who was a teenager but it would be Ditko who would design how Peter Parker looked, and most importantly his costume, whether Pete has organic or mechanical web-shooters and also how he would look swinging across the city. Kirby's art is credited with making books such as the Fantastic Four the most visually creative and distinctive books of the era, and even today the extent of Ditko's role in the creation of Spider-Man is... enthusiastically debated although Lee claimed in The '60s that he would at times leave Ditko to plot out the whole story to his heart's content. In many ways, the classic Marvel era is a useful reminder that it's the quality of the art as well as the quality of the writing that makes a great comic book. Or to put it another way, you can't be Stan Lee without someone else wanting to be like Kirby and Ditko. Remember it was Kirby's capacity to draw out an entire issue in a ridiculous amount of time that made it possible for Lee to work and plan multiple titles at once. It always takes longer to draw out a comic than to write one.
PitfallsAs mentioned above, Stan Lee's writing is full of Purple Prose! And alliterative adjectives! And a high percentage of exclamations, in order to emit an envelope of energy, excitement and enthusiasm! Stan Lee could pull it off, but it's the kind of thing that kinda grates after a while if it's over-used!
It's also noted that many of Lee's superheroes have their origins in radioactivity and toxic waste; Spider-Man's radioactive spider-bite, the Hulk's unfortunate dose of gamma radiation, the Fantastic Four catching a wave of cosmic radiation. Whilst that worked at the time, the 1960s being a period where radioactivity was something that was very prominent on the minds of people at the time, these days using radioactivity as a cause of superpowers is a little hard to sell; it's been overused, subject to wide parody and we're all a bit more savvy about the actual effects of radioactivity now than people may have been back then.
Suggested Themes and AesopsAs mentioned above, Comes Great Responsibility. All of the Other Reindeer is also an important part of these stories.
Potential MotifsStan Lee's superhumans tended to come about due to some kind of accident, usually involving science (and especially radioactivity) in some way. Whilst this may be a bit passé these days, it indicates a concern over scientific advancement; not so much that advancement itself was, but how particular advances could be used for good or for evil. In the comics that Stan Lee wrote, people weren't just given superpowers or born with them, as had previously been the standard; the characters tended to be given their powers either through some bizarre (and often ironic) quirk of fate, and / or had to work hard to earn them. This applies to villains as well as heroes; just as Peter Parker received an accidental spider-bite that led to his becoming Spider-Man, his eventual nemesis Otto Octavius was involved in a lab accident that fused mechanical arms to his back and led to his becoming the villainous Doctor Octopus, and so forth. These motifs work to establish the distinction between the hero and the villain.
The freak lab accidents also had a dramatically effective consequence. Characters given these powers were not always the ideal choices and often had no idea what they should be doing with their gifts at first. Again Peter is a good example as teen superheroes up till this point were usually the sidekicks of adult superheroes or otherwise had an adult figure guiding them (even Billy Batson had Shazam along with a heaping helping of the wisdom of the wisest wiseguy.) Peter by contrast lost his uncle, could not confide in his aunt and wasn't accepted on any superhero teams due to his tendency to act like a jerk. So he made lots of mistakes and had to figure things out for himself.
Notice also how Stan Lee tended to give his superhumans a particular adjective in order to establish how great they were in the mind of the reader. It's not just Spider-Man, it's the Amazing Spider-Man (or, if we prefer the alliterative version, the Spectacular Spider-Man); it's not just the Hulk, it's the Incredible Hulk; the Fantastic Four, the Uncanny X-Men, and so on.
Set Designer / Location ScoutStan Lee set his comics primarily in the New York that he and a large part of his audience were familiar with; Peter Parker lived in Queens, the Fantastic Four and Tony Stark lived in Manhattan, and so forth (although the Fantastic Four were originally based on California's 'Central City', Lee eventually moved them to New York). This showed that superheroes could be placed in the real world. Of course, you might not have been to New York, but you can follow his example by setting your story in your local area — which creates a great potential for interesting stories if it's somewhere which isn't quite as closely associated with superhero stories as New York or a similarly urban American environment.
Costume DesignerThe usual brightly coloured uniforms were present, although Civvie Spandex is also quite common. It's also perhaps worth noting that Lee originally intended for the Fantastic Four, the first heroes he wrote, to just wear everyday civilian clothes, with no 'traditional' super-uniform at all; it was only because he and Kirby couldn't figure out how to effectively pull it off with their superpowers that they put them in the blue jumpsuits made from 'unusual molecules' that they are identified with today. However, just because Stan Lee and Jack Kirby couldn't figure it out doesn't mean you can't...
Casting DirectorParagons need not apply; we're looking for flawed-but-sympathetic persons here. This applies to villains as much as heroes.
The GreatsStan Lee and Steve Ditko's run on Spider-Man. Stan Lee and Jack Kirby's run on Fantastic Four. The list here is endless.
The Epic Fails