First and recommended way is to buy original UMDs and insert into your PSP and enjoy your game on PSP.
The other way is to hack PSP by installing custom firmware on PSP download games from the internet, put them into your PSP memory stick and then play games on PSP. The downloaded PSP games are in ISO/CSO format.
HOW TO PLAY GAMES ISO / CSO ON PSP
Lets learn how to install ISO /CSO files on PSP.
STEP 1 – INSTALL CUSTOM FIRMWARE ON PSP
First of all you need to install custom firmware on your PSP:
PSP 2000, 1000: Install Custom Firmware on PSP
PSP 3000, 2000 TA-088v3: Install Custom Firmware 5.03 GE-C
STEP 2 – DOWNLOAD PSP GAMES (ISO/CSO)
Once you’ve installed the custom firmware on your PSP now download your desired PSP Game (ISO/CSO). Google is your best friend. If the downloaded PSP game is a compressed .zip or.rar file then make sure to extract iso/cso using WinRAR.
STEP 3 – COPY ISO / CSO ON PSP
• Connect your PSP to your computer via data cable. On your PSP, go to Settings > USB Connection.
• Your PSP memory stick will appear as a removable device on your computer.
• Open the memory stick and go to ISO folder. If there’s no ISO named folder then create one and make sure you name it in Caps (ISO not iso).
• Now copy the downloaded PSP Game ISO / CSO file into ISO folder.
• Disconnect your PSP from your computer.