I. Homebrew Guide
First things first, you will need to know what firmware your psp has. This is very important. Simply power on the psp, under settings, go to "System Settings", then "System Information".
Under System SOftware, you will see a version number. If you have a 1.0 or 1.50, you can load homebrew onto the psp. If you have anything above version 1.50, see the F.A.Q. at the bottom of this post for downgrade information.
Installation on v1.0 Firmware:
You will need a usb cable and plug into your psp, then your computer. Power on the psp, go to "Settings", then "USB Connection". The computer should then detect the PSP and show up as a "Removable Disk" (The letter will vary from computer to computer).
All homebrew software on 1.0 Firmware psp must be located under MS:\PSP\GAME (where MS is the memory stick on your psp). You may need to create a game folder if there is not one already. Say, for example you have downloaded a NES emulator. It will most likely come zipped, so first thing you will want to unzip it.
After unzipping the application, somewhere within the unzipped folders you will see a file called "EBOOT.PBP". Create a folder in MS:\PSP\GAME\ according to what program you are putting in there. In this case, we'll call it "NES". Now, simply copy & paste, or drag and drop (whichever you prefer) into the MS:\PSP\GAME\NES folder (replace NES with whatever folder you created.)
That should be all that is required to run homebrew on a 1.0 Firmware PSP. The method for 1.50 Firmware is slightly more advanced.
Installation on 1.50 Firmware:
For this step, I recommend "Sei PSP Tool". It should do everything that will be required (plus more) to get all homebrew working on your 1.5 Firmware psp. You can download it HERE
After downloading Sei PSP Tool, Connect your PSP to a usb cable, then to your PC. Under Settings, go to "USB Connection" and your pc should automatically detect the PSP as a "Removable Drive".
Check to see what drive windows has assigned to the PSP by going to "My Computer" and finding the "Removable Disk".
For this example, we'll say my PSP is given drive F:. Just replace the letter of your drive when you are following this instructions. Have whatever homebrew application you have downloaded unzipped and ready to install on the PSP.
Open Sei PSP Tool, and type a name for your homebrew application. NOTE: Some homebrew applications require you place it in a certain directory, so read the instructions to make sure.
Now, select the EBOOT.PBP file that you want to load onto the psp by clicking the "...", then "From File" after "PBP File". Now, after PBP Unit:, select the drive letter assigned to your psp, here it will be F:.
More advanced users can customize the PBP file with custom ICON0.png and various other images and backgrounds, but that's a later guide 
. The next option you have is to "Hide Corrupted image from list". Although this is not necessary, I highly recommend it. Normally when loading homebrew onto a 1.50 PSP, it will display a "Corrupted" image in your program list, Sei PSP Tool will hide this image for you, which is a very nice feature.
Next, click "Generate", then click "Export to PSP 1.5". You will then get a dialog telling you it has either failed or succeeded, if it fails, read the guide again to make sure you haven't missed a step.
Now you should be able to press O on the psp and go to "Game" then "Memory Stick" and select the program you just loaded using Sei's PSP Tool.
F.A.Q:
Q: Can I run homebrew on a v1.51 or v1.52 PSP?
A: Yes! You can now upgrade your 1.51 or 1.52 PSP to 2.0, then downgrade to 1.50
Q: So, what is firmware?
A: Firmware can also be referred to as the PSP's "Operating System". It contains all the code to make the PSP run correctly. There are 6 known firmware versions as of now, there are: 1.00, 1.50, 1.51, 1.52, 2.0, and 2.01 (JP only right now)
Q:does it re configure your entire PSP to a third-Party setup??? Like a Hack? And what is Homebrew
A:No, the tool won't alter anything on your psp other than creating a couple directories. You don't HAVE to use Sei's PSP tool, but I highly recommend it if you are new to putting applications on the psp.
Homebrew= Homemade applications & games
Wacky mini-golf-based puzzler set in a run-down Nevada theme park.
