Things You'll Need
Instructions
Install your custom PSP firmware, preferably version 3.80 if you have not done so already. Follow the instructions at the PSP Hardware Guide website if you encounter problems.
Press "Select" while at the menu screen to open the system console. Press down on the D-pad twice to select "USB Device". Change this setting to "UMD Disk" by pressing left. Exit the menu screen.
Insert the UMD disk you wish to back up into the PSP. Attach your PSP and your computer with the USB cable.
Navigate in Windows Explorer or OSX Finder to the mounted UMD disk. You should see a file named "UMD9660.ISO." This is an image of the UMD disk in your PSP. Copy it to your memory stick (you may choose to rename it). When it has completed copying, press the O button to end the USB connection.
Return to the PSP system menu and change the "USB device" setting from "UMD Disk" to "memory stick". Play your backup by copying the file to your PSP memory stick. It must be placed in a directory named "ISO" to work correctly.