Brewology

Do you know how old the PSP is? You'll have to make sure it doesn't have a tA-082 mother board in this tutorial.

But, if you do have one of those tA-082 mother boards, then you can use this tutorial.

Good luck.

Here you go, once your done with his guides you can follow this one to upgrade to custom firmware...
http://www.pspbrew.com/forum/viewtopic.php?t=6810

I suggest starting off with 3.52 m33