I know some about the hardware needed for capture and editing, not much about the actual shooting, though.
As far as hardware, you could get a tuner or capture device like WinTV, Dazzle, or All-in-Wonder or a miniDV camcorder with pass-through. (I currently use the last one, but I've worked with others as well.) You will also need a huge amount of hard-drive space dedicated to editing. One hour of DV video is over 13GB! One DVD is 4.5GB. At least 1GB of RAM is also a minimum.
In my opinion, get a miniDV camera. The prices on good point-n-shoot cameras is even lower then when I got mine two years ago. Just make sure it can be used to convert your old VHS-C tapes as well. (I made that mistake once, and I am thankful I realized it before I couldn't take it back and get the other one.)
A good starter program that will capture and edit, (but not burn DVD's,) is Windows Movie Maker. It's a simple editor, it's mostly easy, and free.
Now if you have space and time to learn it, you can try
ZS4 Video Editor. It's free and powerful, but it's taxing on the computer, and it's hard to learn.
I'd recommend to check out this website:
VideoHelp.com They have lots of guides and information that I've found helpful.