Really, really, really basic watercolor editing in Photoshop:
I usually like a clean white background and to brighten my scanned painting. SO, after cropping away all the bad parts, I add a levels adjustment layer. You can move the white arrow to the left to make the whites brighter and move the black arrow to the right to make the blacks darker. I move the arrows until the paper texture disappears and the painting is the brightness I want. You can see the difference in the screenshots. You can also clean up the rest of the background with the eraser too, the white paintbrush OR another levels layer with a masking layer. That’s about it for clean up! How you edit something really depends on what you are going for and your image. This is a good place to start out though.
[ I got a couple people asking how I edit stuff, hope this helps! ]