Instructions
Formatting Your Memory Stick
Go to the "Settings" menu on your PSP home screen, and scroll down to the "System Settings" option.
Select the option "Format Memory Stick" in this menu.
Confirm that you want to format the Memory Stick. This will remove all data from the stick, but reinstall empty PSP folders. If you want to completely empty the memory stick for use outside of a PSP, it is best to do it on your PC.
Emptying the Memory Stick Via Your PC
Plug your PSP into your PC using a USB cable.
Select "USB Connection" in the "Settings" menu on your PSP home screen.
Open up the Memory Stick folder on your PC once your PC recognizes and loads it.
Highlight all the folders or files that you want to remove from the Memory Stick, and delete them.
Press the "O" button on your PSP to end the USB connection and safely remove your PSP from your PC.
Removing Files Individually
Navigate to the file that you want to delete in your PSP home screen.
Press the "Triangle" button to display the file menu.
Select "Delete," and confirm that you want to delete the file. This method has the benefit of allowing you to only remove the files that you want to, and not all at the same time. It is clear on the PSP what each file is, which is not the case when viewing the Memory Stick's contents on your PC.