This link may help you, but your title and question are contradictory, do you want to play ps1 games on your pc or psp? http://www.makeuseof.com/tag/emulating-console-games-on-your-pc-part-1-sony-playstation-1/
first of all confirm it that are you talking about PC or PSP. Your post title says PC while your post content says PSP. It is confusing me. So, if you want to play PS1 games on PC, try any emulator. Search the web, there are a lot of emulators you can find.