You will need a memory stick and you'll need a USB cable that has a "Mini-B" connector on one end and a "Standard-A" connector on the other on it as well. Plug them into the appropriate places on your PSP and PC.
From the PSP go to the top of the settings list and then select "USB Connection". Your PC should detect a new "Removable Disk Drive" that you can then access.
Then format the memory stick. In order to use it on the PSP you need to.
Put the files into whatever folders you see fit. You could make a folder called RIN (for example the RIN emulator) and put your emulator in there. Then make another for your GB/GBC games, etc.
When your done with your work you'll need to press X to exit the USB mode. The disconnect the PSP from the PC. Other than that, should be fairly simple. The places you need to connect the USB cable should be obvious. So hopefully I won't have to explain that.
The only one that I know anything about is RIN. And that one is easy to install too. All you have to do is create a folder on the memory stick for RIN and one for your games. Then navigate from your HOME screen on your PSP to the folder RIN is in and run it. That will at least give you Gameboy and Gameboy Color. RIN does have an English FAQ on their site.
At any rate here is a link with some DLs of emulators designed to work with the PSP. Several of them were made by Japanese teams that may or may not have English FAQs, etc. (or worse no homepage links) RIN does, but I have noticed with others this is not so. So, good luck to you.
Check them out if you haven't already. And if there are FAQs for them by all means PLEASE READ THEM.
Emulators for the PSP
I have no idea about firmware needing to be modded? Anyone know what he is referring to?