You can go about a couple ways:
1) get a video capture card such as: ATI TV WONDER capture card about $50, the Dazzle Drive is about $60-ish..., or even Pinnacle about $60-100-ish. That allows you to hook your vcr/dvd or even tv to your computer and capture video. These can be found at Bestbuy, circuit city, comp USA etc. There are also other brands. This will be the easiest way to go about it.
2) Rip the video from the whole dvd or sections of it to you your hard drive. Check out :
http://www.videohelp.com/. THey have every kind of guide imaginable. You can then download tools to rip directly from the dvd to your hard drive in *.avi or *.mpeg (almost every type of format).
ON the left hand side under "how to" section click "guides". They will have a scroll menu to choose your conversion. In your case it would be "DVD to AVI" or "DVD to MPEG." Though video converting can take a long time. (free but may take some time)
There are tons of other ways, but I believe these are the most common ways of doing so. The first approach is faster though more expensive, the second is free but time consuming... It's a give-give situation.
But after you rip or capture the video you need a video editing program such as Adobe Premiere which is quite expensive, apples' Final Cut pro, Pinnacle studios; their capture card sometimes comes w/ the software though you can buy it separately. HP, dell etc... they all have video editing programs. There are tons on the market. Just do some research to know what your getting. On average I say it's safe to say that video editing programs can range from $70-150 and sometimes higher *cough adobe*
But i can say that both Pinnacle Studios and Adobe are the most popular. Though I believe the pro's usually use adobe, though don't take my word on it, I may be mistaken. WHen it comes down to it, both are great editing programs. Though money wise, Pinnacle Studios may be your best bet.
Hope this helps.
edit: None of these methods will mess up the original dvd. Dvd ripping means copying the dvd(video) to your hard drive.