PSP Custom Firmware resources
Reasons to install
There are many things you might want to do on a PSP that requires installing custom firmware, also known as CFW. For example, to turn your UMD files into ISO files that can be loaded in PPSSPP.
Custom firmware is also important when reverse-engineering the PSP in order to fix bugs and implement new features in PPSSPP. It lets you run psp-link, that lets you load homebrew apps over USB, which is useful for running hardware tests.
Installation guides
There are many models of the PSP and several types of custom firmware that are compatible depending on the model and have varying features. There are permanent versions, and others that disappear when you reboot your PSP.
For purposes of UMD dumping, you probably don't need to install a permanent CFW.
Anyway, there are many guides online, the below is an attempt at maintaining links to reliable ones: