Visit the Internet Movie Database (IMDB) and access the IMDB Plots Browser. You can search there for a word or phrase that is integral to the classic film plot, for example "World War II" or "little girl beauty pageant." Search the Turner Classic Movie Database by keyword. TCM has over 163,000 movie titles, spanning from 1890 to present day.
Go to AllExperts.com and access the Classic Film/Experts section. You will find a list of movie aficionados who have signed up to answer user questions, with their areas of expertise clearly listed--silent films, Christmas movies and others. The experts are ranked for their knowledge, clarity, timeliness and the politeness of their responses.
Join a classic movie forum and post the story of the movie, asking members if they know the name. There are many savvy old movie buffs online who would be happy to point you to the title of the film you seek. Two popular sites that feature lively film forums are classicmovies.org and TCM's Classic Film Union.