Step 1:
Check your PSP model number. Using a PS3 controller with the PSP requires a USB port on the PSP itself, which is only available with the newly released PSP series 3000. Previous PSPs have a different kind of port.
This is incorrect, all models of PSP barring the Go have the same mini USB port.
Step 2:
Plug your USB cord from the PS3 controller into the USB port on the PSP. This is the cord you traditionally use to charge your controller. Plug one end into the top of your PS3 controller and the other end into the PSP.
Again this is incorrect and not humanly possible. The cable used to charge the Dual Shock 3 is a USB to mini USB. Both the PSP and the Dual Shock 3 have the same mini USB port.
Step 3:
Turn on controller support under the "Settings" menu. The PSP will automatically recognize that an external device connected to its USB port, so all you have left to do is navigate to the devices "Settings" menu and select the controller from the "Devices" menu. After that, simply prop your PSP up where you can see it and use your PS3 controller to play to your heart's content.
Again this is not possible as the PSP 3000 doesn't have a "Settings" menu, nor a "Devices" menu.
If you activate the USB Connection on a PSP 3000 you are not able to use the PSP at all.
As I have already stated, the only way to use a Dual Shock 3 on a "non Go" PSP is via PSP Plus, and the only game that supports it is Resistance Retribution.