Use canned air to spray out the crumbs and dust. Then spray and wipe with electronics cleaner. If you don't have electronics cleaner, you can also use 190 proof alcohol.
I would clean it with a little bit of windex, and a dry cloth. Do not scrub too hard or you may ruin it. You could also try cleaning it with a dry shamwow. Whatever you do be careful not to rub too hard or you will break or scratch the screen.
You can try canned air they sell it at most department stores or you can take it in and they will clean it for you or you can check and see if they sell a cleaner just for that.
Simply use windex, or a glass cleaining agent and spray it on a toothbrush. Rub the toothbrush on small parts of the psp, and use a cloth for the rest.
I have been seeing adds for a thick jell product designed to clean in between the buttons of small electronics. They show it being used on a key board, for example. I have not been able to find it yet, however.