In Linux a program does not reside in it's own folder like Program files in windows or Applications on a Mac but the files are spread accross the system. Once installed you can use the PyGame library to write your games.
In the PyGame documentation you can read all about how to get started: http://www.pygame.org/docs/
== If it's not broke... I'm not done fixing it! ==
Pygame is already installed for python (Python 2) and should work fine. If you are using python3 (Python 3) you have to install it. There is not any ready-made package for that so it will be a more complicated process than using apt-get. You can find instructions somewhere on this forum.