There are a few dependencies for installing but here is a list which works. The link to the original which I have mostly copied is here:
The full list of instructions below should do it:
sudo apt-get install python3-dev python3-numpy libsdl-dev libsdl-image1.2-dev \ libsdl-mixer1.2-dev libsdl-ttf2.0-dev libsmpeg-dev libportmidi-dev \ libavformat-dev libswscale-dev libjpeg-dev libfreetype6-dev
sudo apt-get install mercurial hg clone https://bitbucket.org/pygame/pygame cd pygame
python3 setup.py build sudo python3 setup.py install
And voila you should have it. To test:
python3 >>>> import pygame
If it throws an error then pygame has not installed properly.