One method is framing the questions to get the answers you want, typically with loaded questions.
Close, but not the same, is where you don't care about the answer, you just are using the questions themselves to sway people: the poll is propaganda or rumormongering masquerading as opinion polling. Example: "Do you believe we should retreat and let the enemy conquer the world? (Yes/No)". Another example: "Would you be more or less likely to vote for Candidate X if you knew he was a convicted murderer?"
Another is polling people when you already know how they will answer, that is, only polling people who might already have the opinion you want. For example, polling only rich people about whether welfare expenditure is too high.
Also there is polling people to identify their opinion personally in order to discover exactly who has what opinion, which is the opposite of legitimate polls where people are only identified by the demographic, not by name.
Subtrope of Lies, Damned Lies, and Statistics.
- Happens all the time on Wikipedia. Many people seem to think they can change the (nebulous) rules and force all other editors to do what they say, simply by holding a small biased poll on the matter. One of the more famous ones was a policy proposal to outlaw sarcasm.
- Google Docs offered a survey which was surprisingly long, and the bulk of the questions were asking if the user was aware of such-and-such feature. It seemed it was at least as much about making the surveyed users aware of those features than it was about gauging how many people were using them, which could presumably be accomplished without a survey since Google Docs runs on Google's own servers.
- Any Twitter poll that says "RT for yes, fave/like for no". Since only one of those options is a signal-boost, and people generally follow people whose opinions they share to some extent, you can bet more potential "yes" voters are going to see this than "no" voters.
- Parodied in Lowering the Bar, in regards to posthumously pardoning Jim Morrison for a public indecency charge. The website's opinion poll offered readers the choice to vote "yes, we think Jim Morrison should be pardoned" or "no, I either don't know who that is, do not like music or other kinds of fun, or think it is more consistent with American values to not cheer up Morrison's aging father by clearing his son's name of a trumped-up charge that was President Nixon's idea in the first place."
- One episode of Yes, Prime Minister had Sir Humphrey demonstrate how this works by asking Bernard two separate series of questions, one leading to the obvious conclusion that compulsory military service would be a good thing and the other leading to the obvious conclusion that compulsory military service would be a bad thing.
- Parodied by Stephen Colbert: <insert person>, Great <relative position> or Greatest <relative position>? (George Bush, Great President or Greatest President?) And trying to Take a Third Option by flat saying the subject wasn't great at all just gets you "I'll just put you down for 'great', then, because that's not as great..."
- On Parks and Recreation, Leslie tried to get public support for building a park, by presenting the question to the public as "Wouldn't you rather have a park than a storage facility for nuclear waste?"
- Demonstrated on Penn & Teller: Bullshit! in an episode about statistics. One guest shows how polls are slanted to get a certain answer by asking questions of the same person and getting conflicted answers.
- Adam Carolla of The Man Show was able to convince over a thousand women to sign a petition to end women's suffrage, though this might be more related to Viewers Are Morons.
- Calvin of Calvin and Hobbes likes to confront his dad with polls of the 6-year-old and tiger populations of the house. While these invariably show a landslide of popular opinion, his father inexplicably remains unmoved.
- One Doonesbury strip had a reporter at a George W. Bush museum interacting with an exhibit designed to show why Dubya wasn't the Worst President Ever. The questions went [Allow Saddam to somehow use WMD's he didn't have to take over the world] or [Invade Iraq again].
- Likewise with PiQ's (replacement for Newtype USA) article regarding fans' opinions on their new format. The fact that it was called the "Cheese and Whine Party" pretty much guaranteed that anyone who didn't like it wasn't exactly going to get much sympathy.
- Back when WWE Raw did fan polls, must of the options were so heavily pushed so as to not ruin stories. The best example, however, was when the audience was given the choice of three different match stipulations: Extreme Rules, Falls Count Anywhere, and No Disqualification.
- A Peanuts special ("You're Not Elected, Charlie Brown") had Lucy taking an opinion poll to see if Linus could win the school election. Naturally, she intimidated everyone into saying they would vote for him and she thus concluded that he had a good chance.
- There was a famous Real Life example to show how people will sign any petition if it's worded the right way. People were asked to sign a petition to ban the substance dihydrogen monoxide - used in industry with almost no regulations, used by various kinds of criminals, capable of killing humans and other animals, able to corrode iron... Of course, anyone with a basic knowledge of chemistry should know what molecule has two hydrogen atoms and one oxygen atom.
- One infamous push poll was created by Karl Rove while working to get George W. Bush nominated for president over John McCain. "Would you be more likely or less likely to vote for John McCain for president if you knew he had fathered an illegitimate black child?" Theoretically this is a moot point, because he didn't — but the poll put the idea in people's heads, without technically making a provably false accusation.
- Moral philosophers do this on purpose, and it is amazing how they can completely change someone's answer to the most fundamental questions of life by changing only the way exactly the same question is phrased. Which is why education is important in the first place.
- When Kay Hagan was running against Elizabeth Dole for a North Carolina U.S. Senate seat, potential voters received calls from a company which was taking a poll. One of the questions, "Would it affect your vote to know that Kay Hagan is associating with and taking money from atheists?" This question and some others like it soon made it clear that the "polling company" was not legitimate, but was only asking questions to raise doubts about Hagan. Dole's campaign also ran a TV ad implying that Hagan, who was a former Sunday school teacher, was an atheist. By the way, Dole lost the election.
- A rumored Real Life example that led to the break-up of the Soviet Union. The politicians interested in splitting the Union polled the general public with the question "Do you want to be independent?" Obviously, nobody is going to answer "no". They used the answer to justify the break-up.