I've downloaded the latest PSP firmware to my computer now I just need to know where to put it on my PSP so I can update it.
Connect to the PSP with a USB cable and put BOOT.PBP in the folder PSP/GAME/UPDATE - it is important the the folder names are ALL CAPITAL LETTERS.
Then, with your PSP charged (and preferably still plugged in to avoid battery glitches), go to the games section, select Memory Stick and then select your update. Follow the update instructions and let it do its thing.
Place the update file "EBOOT.pbp", inside the following folder on your PSP:
If it's a PSP Go, place it in the system memory, not on the memory stick. Then navigate to the PSP's game menu on the XMB menu and select update. Make sure the PSP has about 50% battery and is connected to a power source, just to be on the safe side. If it powers off while it's updating, it can be a nightmare to fix it.