The PSP is a great handheld system for emulating older consoles. According to Wololo, practically all consoles from the first seven generations have a PSP emulator available.
Install custom firmware
Almost all PSP emulators require custom firmware to run. To install the firmware, first update the PSP to the most recent firmware released by Sony. Connect the PSP to a computer with a USB cable, and move the firmware to the "PSP/GAMES" folder on the memory stick. Disconnect the PSP, and boot it up. The custom firmware can now be run from the "Game" menu.
Download an emulator
Choose an emulator for the desired console. Download it, and install it on the PSP by copying the emulator files from a computer to the "PSP/GAMES" folder on the PSP's memory stick. Most emulators require you to boot the custom firmware every time they are used. Even if they have been properly copied to the PSP, they do not appear in the menu unless the custom firmware is loaded first.
Add emulated games
Find games for your emulator in the form of ROM or ISO files. These files are usually installed by copying them to the "PSP/GAMES" folder, but some emulators require the creation of a separate folder or directory. Check the instructions that come with the emulator for detailed directions.