Check your local stores for flyers and listings for events in the area. Comic book shops, video game stores, and anime/manga stores will often advertise events with posters of upcoming conventions in their windows, or on their walls.
Read an anime periodical such as Otaku USA Magazine. Events are often advertised in the back section of magazines. Their website, Otakuusamagazine.com is a handy resource for anime-related events.
Attend the Anime Expo, which is the biggest anime convention of them all. The Anime Expo is hosted at the Los Angeles Convention Center annually. Advertisements for smaller events are often displayed at the Anime Expo.
Join an anime group or fan club. Members of these groups may be a reliable source of information for local anime events.
Search for events on the Internet. There are a few online resources can help you find an anime con, including AnimeCons.com and UpcomingCons.com. Though smaller events may not be listed on the Internet, both sites are reliable sources of information for larger conventions.