Hypothetically the best thing to do is search the filename on a search engine, and replace the video file type with .ass or .srt
Say you hypothetically come into contact with a film like The Good, The Bad, The Weird, but you don't have subtitles for it. The filename is bfs-tgtbtw-cd1.avi, but you'd like to get subtitles for that specific movie. So you type it in on google, "bfs-tgtbtw-cd1.srt megaupload.com" or any other file sharing site you hypothetically know of. Most likely you'll get the correct subtitle set for that specific film.
Now, if you don't want to do this, you can always re-edit the subtitles. Count how long it takes after something is said, or before something is said, for subtitles to appear. Let's say 3 seconds after the audio plays, the subtitles appear. Well, that's too late and will get annoying for longer speeches later in a movie. So you'd open up a subtitle program that has a mass-timer edit, I'm not sure if Aegi-sub has this option, but there are a lot out there. You'd highlight the timeline for all subtitles and essentially it should let you type in something like -00:03 to make all the Subtitles in the film/video, go back 3 seconds in time, to sync up with a film/show, whatever you downloaded.
Though, I think this takes a bit too long as you don't know if all the subs are out of sync, so I'd really just suggest looking for the correct subs for your video.
Hypothetically of course.