Depending on how elaborate your edits are going to be, you can use most of the common editing programs, like Adobe Premiere Elements, or Corel Video Studio.
Two others you might consider would be Womble Mpeg Video Wizard DVD....a ridiculous name, but a good program for editing mpeg2(the video codec found in dvds) since it doesn't require re-encoding the whole video when making cuts. And VideoReDo TV Suite, which is very similar in function to the Womble program.
I believe all of these have free trials to test the programs. I know the Womble and VideoRedo programs are fully functional for the length of the trial....haven't examined the terms on the Adobe or Corel programs to know for sure on those.
You will need to rip the entire contents of the dvd onto the hard drive first...it will be faster working from the hard drive rather than the optical drive. Then edit, then burn to a new dvd.