There are two nice ways to install Python packages on Ubuntu (and similar Linux systems):

sudo apt-get install python-pygame

to use the Debian/Ubuntu package manager APT. This only works for packages that are shipped by Ubuntu, unless you change the APT configuration, and in particular there seems to be no PyGame package for Python 3.

The other option is to use PIP, the Python package manager:

sudo apt-get install python3-pip

to install it, then

sudo pip3 install pygame

to fetch the PyGame package from PyPI and install it for Python 3. PIP has some limitations compared to APT, but it does always fetch the latest version of a package instead of the one that the Ubuntu packagers have chosen to ship.

EDIT: to repeat what I said in the comment, pip3 isn't in Ubuntu 12.04 yet. It can still be installed with

sudo apt-get install python3-setuptools
sudo easy_install3 pip
sudo apt-get purge python-pip

After this, pip is the Python 3 version of PIP, instead of pip3. The last command is just for safety; there might be a Python 2 PIP installed as /usr/bin/pip.