Premiere Pro is able to read the video content of a DVD disc provided it is not protected (such as commercial movies). Then in Premiere you can do whatever you want regarding edits, titles and audio.
You will probably lose any menu from the original DVD (if any).
After you have done your edits, you will not be able to update the original DVD nor output to a new DVD from Premiere, as it does no longer offer that functionality since version 6.0, due to some licensing issues.
Anyway, you can export an mp4 file and use in a memory card or upload to youtube / vimeo.
If your video editor of choice does not read directly the DVD, then you need first to convert it using a "DVD ripper"