Ok, I do home video editing and creation as a hobby. Mostly to capture life moments and such. However, this is what my experiences have to offer.
If your movies are not copy protected. You can use a tool like Nero Recode to convert the DVD to a format you can edit (ie moviename.avi). After you have done that you can use the free tool Windows Movie Maker (part of Windows XP) or you can use Nero Vision (part of the same suite you get recode with). Nero's product is rather affordable and ok to use. If you really want to get into editing and want to spend a lot of money, you can buy Adobe Premier to edit with. After you have edited the video content and created the outputs as AVI files (or something similar), you need a way to put those back on DVD. I personally use either Nero Burning Rom (another piece of the Nero Suite) or Adobe Encore (another piece of expensive software). So in short that is what I use to edit video and put it on DVD. If I had to pick one to recomend to you it would be Nero's Suite of products. You will get the most bang for your buck. You can buy Nero at Best Buy or similar store or online at
http://www.nero.com