I'm the same way. First computer I was ever inclined to coddle and stroke (at least while no one else was around).
The answer to your question is not as easy as making a disk copy of the DVD and copying to a blank one in toast. Contents of DVD movies are copy protected after all. They're not going to make it easy for you. It will entail ripping the contents into a new format, processing it and re-encoding it, then burning back onto another disk. You're going to loose some quality doing this as well. Since I'm not an expert at it, I'll leave the full details to someone who is.
In the meantime, I'd recommend a little
google to familiarize yourself what's in store for you.
DVDRHelp.com is also a good place for info.
There are more immediate ways to get a copy of a DVD movie if you're not wanting to purchase another copy. There are DVD player/burners, but I know, it's not as fun and why get another piece of equipment, right?
Cheers.