A good place to start is the
Guides off the main page. The vast majority of questions can be answered by reading through the material there.
Basically, you're going to need two things: a way to get the footage you want to use onto your computer (*hint* downloading it from the internet is should in almost all cases not be this method) and software to convert and edit the footage. For the former, you'll need a DVD-ROM drive and a bunch of free software (covered in the guides) or a capture card of some sort (if have VHS tapes and not DVDs) and for the latter, the majority (I believe) here use Adobe Premiere, but it at best is going to be several hundred dollars. There is a trial version available from Adobe that you can use for 30 days to see if you like the program and think it's worth buying or if you want to investigate something else. That's usually enough time to make one video and see if it's really for you. There are other options (haven't checked in a while to see what progress has been made on the Linux AMV guide), but Premiere is probably the route you'll want to check out first.
Read through the guides, and come back with any specific questions. Before actually asking them, run a search of the forum (including all the 'video' forums is generally good) to make sure your question hasn't already been asked and answered a number of times best represented in Scientific Notation. People in this forum and the other 'help' forums are generally quite willing to help out, but are much more likely to help people who have at least tried to help themselves first.