Hey there,
There are quite a few things you can do...it just depends on how "good" you want the production to be on your audio recording. You can go as simple as plugging an inexpensive microphone into the mic jack on your computer and recording into sound recorder (not recommended!) to coming up with a very good quality production using a Digital Audio Workstation program like Pro Tools, Cakewalk or Cubase.
Considering you probably don't want a crash course in DAWs just to make an overlay for your DVD project, I would recommend you look into something very simple to record with, like Apple's Garage Band (if you're on a mac) or Cakewalk Guitar Tracks. It might have a slight learning curve associated with it, but it will be worth it to see the leap in quality of your song. If you're going to do it, do it right!
If none of this appeals to you (or you have some time constraints), you can simply go to a local recording studio and lay down your track. This will be the easiest method (although it probably has a higher price tag). You simply need a wav file or mp3 in order to take advantage of it in Windows DVD Maker.