For really basic videos, use Windows Movie Maker2. If you have windows XP, you most likely have WMM2. Check around for it.
For fancy-shmancy stuff, you'll want Adobe Premiere(which is very hard to use).
To get the footage, don't download it. Get yourself a DVD ripper from the internet. Try DVD2AVI.
Also, if you can help it, don't use mp3s, rip the music from CDs. Windows Media Player can do this.
Also, when ripping DVDs, make sure you set it not to "interlace" the footage, or you'll get some nasty quality.
For a real in-depth guide,
http://www.animemusicvideos.org has a bunch of guides. Also, if you don't have an account, get one. Download one of the top 10% videos to see what a good AMV should be like.