DISCLAIMER: Me or PSPmod has no responsibilty of you screwing up your PSP. ORIGINAL LINK HERE
To do this you'll need the following:
• 1 can of Brasso or Silvo (Both work just fine, but I use Silvo due do how much I use it for everything else).
• 2 rags or other type of lintfree cloth.
• A few LCD cleaning wipe or alcohol wipes.
There are two way of doing this, but since one voids the warranty, I won't go into detail on it. All you do is take the rag and put a few drops of polish on it. Then rub it in a circular motion in the clear area of the faceplate. Do this untill about half of the scratches aren't noticeable, then rub the other direction.
Once all the scratches aren't visible, wipe the polish off the PSP using the clean cloth. Be sure to wipe up, away from the buttons, or you'll have a dust problem with the dried polish getting inside the PSP. Once it's all cleaned up, allow the residue to dry and clean it up with an alcohol wipe.
Now your PSP is scratch free and all clean.