How do American people find movies and theatres?

Fandango is really good. In my area (SF Bay Area), Fandango has nearly complete coverage of local theaters. But I think that it's not as complete in other geographies.

In my part of the world (Los Angeles)... Sometimes I see a billboard. Sometimes a bus stop draws my interest. Sometimes ads are on buses. Sometimes through newspapers and other printed publications, but not very often. But, usually I know what's coming up through previews I see at the theaters. As for the theater, I usually go to the one closest to my house.  Just typing in 'movie showtimes' into Google let's me know what time the film will be starting.

I usually use the Fandango App or website.

I use a combination of Rotten Tomatoes and a Google search. And NPR.

At the risk of doing an unpaid ad for their services, I've been a big fan of Fandango (http://www.fandango.com). They usually have pretty comprehensive movie listings, often even giving showtimes for theaters that don't use their ticketing services.

you can check in http://showtimes.surfolks.com/, this provide option to view movies running near you. Mobile compatible, Android app also available.