It's difficult. Unless you happen to recall the same details about the story, most identification questions require a lot of experience.
First, you can try googling. Do a web search, or (for written works) a search on rec.arts.sf.written (if you know of a good search engine for that, tell me — Google Groups search has been painfully unhelpful for several years). Sometimes the asker didn't google enough. Not all askers have searched as much as they should have. Also, knowing to weed other candidates can help. Even remembering some other story can help!
If the author remembers at least part of the name, search on ISFDB.
The type of plot or some other characteristic might remind you of a particular author even if you haven't read that particular story. It's a lot easier to search or research an identification question if you know the author. Even a wrong guess can help the search if someone else has made that wrong guess before.
If you can't solve it yourself, advertise. Ask your friends. Retweet it. Ask on rasfw.