One good thing to learn is about extracting foreground from a solid background. Then you can replace the background with a clean solid background, and save the foreground. If you don't have any Photoshop or equivalent experience yet, I'd suggest just learning some basic skills first. I'm sure Youtube has some decent tutorials. I've been using Photoshop for awhile personally, but I used a book a couple years ago to fill in some knowledge gaps.
Edit: It might be fun to make a 15 minute or so Youtube video just running through the process of cleaning up a scan.