First use DVD Decrypter to rip the DVD's to your hard-disk.
Next use a freeware like VirtualDub or a commercial software like Dr. DivX to convert to avi.
You can get an excellent guide on using DVD Decrypter here
http://www.doom9.org/
If you intend to convert a lot of movies to avi, you might consider investing in Dr. DivX which is really easy to use.
If you don't want to spend any money, you can use VirtualDub. Guides on how to use it are available on the site mentioned above.
Get DVD Decrypter here
http://www.dvddecrypter.com/
Get Dr. Divx here
http://www.divx.com/divx/drdivx/
Get VirtualDub here
http://www.virtualdub.org/

When you convert to avi, you can use 1-pass or 2-pass. 1-pass has average quality and 2-pass has better quality. But choosing 2-pass will roughly double the required time. You might want to consider this carefully as encoding with 1-pass on a P3 itself will take a REALLY REALLY REALLY long time.
If you don't understand something in the guides, feel free to ask.