Ohhh... firmware updates :D they're easy. Just charge your psp up entirely, then leave it plugged in. If you have wireless, go to Network Update (renamed System Update on newer firmware) on the first icon on the crossbar, and that'll download teh newest firmware for you. If you don't, go check the psp site... you'll find a downloadable and instructions there to put it on your psp via USB.

Then (leaving it still all plugged in) you just run the update and let it do it's thing. Easy as that. ^^