I use the screencap/record function of any emulator that I am using (I don’t use a separate program like Fraps) to take the caps, and then I clean them up in Photoshop CS6 or CS5 (depending on which computer of mine I am using at the time.)
A lot of the reason why my caps look very clean and clear has to do with the settings I’ve created for the emulators that I use. But removing blurs and cleaning up contrast and curves in Photoshop helps a lot, too. I never alter their colors because I like to keep them as true to the nature of the game as possible. That also makes it easier for people to use my caps to make their own graphics and edits in the long run.
This is just a general idea of what I do, but if you would like more detailed steps let me know and I will answer privately, as it takes up quite a bit of space to explain and I am sure not everyone that follows me cares.