The first law of marketing is, you can't change people's minds cheaply. If you are marketing a film and you do not have a huge marketing budget, your objective is not to find the people who need to see your movie. It is to find the people who want to see it. When enough people who want to see it can find it, a lot of other people will find it too.

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So the first step in marketing a film is making a list of all the people who will enjoy the film. Oddly, that is often easier said that done. People have an instinct that drives them to think in terms of demographics. Black men under the age of 25, married women over 40 and kids 8-12. This is entirely the wrong way to identify your target market. Instead, think of issues and causes your film addresses. For example, JUNO is a film about a pregnant girl deciding to have a baby and giving it up for adoption. BIG FAT GREEK WEDDING is about a marriage within the greek community. PASSION OF THE CHRIST is about the crucifixion of Christ.
Now, think about what people who have an interest those issues or causes are likely to look up online or read in a new paper or find in a magazine. Your marketing objective should be to put yourself where those people look. In the case of PASSION OF THE CHRIST, Gibson ran previews of the shows in churches. BIG FAT GREEK WEDDING opened in greek communities on the east coast. People knew JUNO was about an unwed mother long before they knew anything else about the film.
The objective is not to tie your film inextricably to a single cause, it is to put your film in front of people who will find it relevant to things they care about. Note that you may well decide to put your film in places where people who will hate it lurk. When O'Reilly attacked Fahrenheit 9/11, I'm sure Michael Moore wanted to send him roses. The controversy stirred up by talk shows over that film guaranteed that everyone nationwide heard about it. Though a substantial majority of folks who watch conservative news shows were not customers for Michael Moore's movie, many others forced to watch with them, were.