ExcruciationX, from our forums 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...
1. Download Ex's pack in his signature.
2. Extract it.
3. Put it in the PSP/GAME/ folder or PSP/GAME150 if you are on 2.71 SE or 3.02 OE.
4. 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.
If you have any questions or troubleshooting, then post in this thread stating your problem. Someone WILL help you.
EDIT: Since people didn't like this one, I have uploaded the old one which is pretty much the same thing on to YouTube (Thank's Ninja).
EDIT 2: This does NOT work with any firmware above 2.80! EDIT 3: Please give me rep if you like it.