I have owned my PSP for a while now and I remember one of the main reasons why I wanted the PSP was because of all the cool hacks and emulators that could run I the PSP. But in order to do these cool hacks you needed to downgrade the PSP to 1.5 version firmware or run a custom firmware.
A few years ago downgrading the PSP was a little more trickier than it is now. Back in the day only certain firmware could be downgraded so if you did not have the right firmware you were out of luck. And the chance of bricking (turning it into a paper weight) a PSP was far greater and riskier than it is now I think.
Now there are custom PSP firmware available allowing you to run homebrew applications and keep all the functionality of newer PSP firmware. Right now I am currently running a custom firmware on my PSP and it’s great.
I would not be able to go over how to downgrade your PSP because there are so many variations of firmware, downgraders, and custom firmware out there. And this stuff changes constantly so things get outdated very quickly. But I will tell you where to go if you want to downgrade your PSP. There are two places I visit when I need to downgrade or update my custom firmware. These two sites should have all the information you will need to hack your PSP.
The first place I go to is PSP Updates, this site has a great community of PSP owners especially in their forums where there are tons of hack your PSP tutorials for just about every version of PSP.
The other one I go to is PSP Hacks. Very simple site that has all the latest custom firmware and downgraders. Although not as much instructions and guides as PSP Updates.