Clean or Refinish The Disc
A game disc can be cleaned with canned air sprays and gentle wiping with a cotton ball dipped in a half water/half alcohol solution. Use an official refinishing kit if you need to repair a scratch. After the game is cleaned as much as possible, try it again in the same PSP.
Try a New Game
Place a clean and unscratched disc into your PSP. If the new game works, the problem may be with the first disc. The disc may simply be defective and will need to be returned or replaced.
Broken PSP
If no discs work at all, the PSP reader is broken and the machine will need to be sent in for repairs. Though there are more affordable third party options, sending it to Sony will get it done properly and will not void your warranty.