Check the filmography for any of the film's leading actors. Find listings of actors' film credits on free movie fact sites like the Internet Movie Database (imdb.com) or Film Safari (filmsafari.com). For example, search on Chevy Chase on imdb.com and you'll get an entire list of his movie and TV work. In all but a few cases, the sites provide a link to the film that will include a description of its plot, the other cast members and more. An actor with Chase's experience will have a long list, so if no titles ring a bell you may click on several films. Eventually, you'll find out he played a reporter/detective in "Fletch" and "Fletch Lives."
Search for the movie title with a keyword search. This will work if you know just part of the title. Use a movie-specific search rather than a general internet search engine; this could be a film fact site, or a catalogue search for a public library or website that sells or rents movies.
Find the movie by reading title lists for that genre. To narrow it down, try to guess what decade it was made in by comparing elements like style, clothing and hairstyles, music and special effects to other movies whose dates you know.
Look at awards listing if you know the film has won or been nominated for any. Many major film awards have official databases listing all records of nominations and wins on their official websites, including the Academy Awards (oscars.org), the Golden Globe Awards (goldenglobes.org) and the Sundance Film Festival (sundance.org).
Search by entering unique catch phrases, quotes or character names within the movie. The more memorable and distinctive words you can think of, the better. For example, even a Google search for "A failure to communicate" will quickly give you "Cool Hand Luke."
Try a human-powered search. If all other catalogue and database searches fail, post your question to a related internet forum (especially if your movie is indie or from a cult genre). Ask people who deal with movies a lot as part of their vocation, such as librarians, clerks at a video store, or film students.