ExcruciationX, from DCEmu has made a tutorial that is meant to help people with the install process. Here are the steps to upgrade to the recently released firmware...
This officially worked for me -- I used Ex's pack --Harry1
1. Download Ex's pack in his signature. (Download 3.03_Installer_pack.zip from FileFront!)
2. Put it in the PSP/GAME/ folder or PSP/GAME150 if you are on 2.71 SE or 3.02 OE.
Run it. If your battery isn't charged an plugged into the wall outlet, then hold Triangle + L to bypass it. The pack has everything needed for installation! I would also recommend watching the video while you upgrade, so you know what your psp should do.
Heres the Youtube Video --
Via DCEmu