These PyGame installation instructions presume you're running the official Raspbian images on your Raspberry Pi (and it works for any Debian-flavour Linux image).
First, ensure your Raspberry Pi is connected to the Internet.
Next open an LXTerminal window and type the following command:
sudo apt-get install python-pygame
Enter the password you used to login in with, and reply
'y' to any prompts.
Now you should be able to run any PyGame program, or create your own.
A post from my Learn Python on the Raspberry Pi tutorial.