Can a sd card fit in the psp?

Yes,

But you must Format the memory card.

You can do this by inserting it in the PSP then go to

Settings/ System Settings/ Format Memory Stick

This will delete everything on the memory card and make folders for the PSP.

Basically it formats it so that the PSP knows where everything is such as MUSIC, VIDEOS, or PICTURES.

Again it will work at no risk. But I'm warning you it will delete everything on the memory card so if it's your camera's memory card you might want to transfer the Files to another storage device or computer.