Instructions
Select "Network" from your PSP's main menu.
Choose "PlayStation Store." The Sony online PlayStation Store will load on your PSP's screen. Select the "Game" menu option from the top side of the screen.
Choose the "PSOne Classics" option. This shows you a list of all of the PlayStation 1 games that are playable on your Sony PSP. Select the game you want to play. From its dedicated page, select "Buy Now."
Choose "Confirm Purchase." This will charge your PlayStation Network account the designated price for the game (PS1 games cost anywhere from $4.99 to $14.99 depending on the game, as of January 2011). The game will then be downloaded to your PSP and you can play it without installing custom firmware.