Firmware 1.51 or 1.52 - If you have a PSP with version 1.51 or 1.52 firmware and you want to play homebrew:
1) You will first need to upgrade your PSP to version 2.00 so that you can use the 2.0 -> 1.5 downgrader. To do this, first download the 2.00 eboot file [here]. This file will be used in the next step.
2) Next, upgrade your PSP to version 2.00 using the 2.00 eboot you just downloaded with the upgrade tutorial found on Sony's site [here]. *NOTE: DO NOT use the PSP's network update feature as it will upgrade you to 2.01 making it impossible to downgrade back to 1.50!