You don't need to install Python 3.4 because there's a version of pygame ready for 3.5. Open a terminal (press Ctrl+Alt+T), and run:
sudo apt install python3-pip
pip3 install pygame
The last command gives the output:
Downloading pygame-1.9.2rc1-cp35-cp35m-manylinux1_x86_64.whl (10.0MB)
100% |████████████████████████████████| 10.0MB 54kB/s
Installing collected packages: pygame
Successfully installed pygame
cp35, which means it's for Python 3.5. This can be verified:
Python 3.5.2+ (default, Sep 22 2016, 12:18:14)
[GCC 6.2.0 20160927] on linux
Type "help", "copyright", "credits" or "license" for more information.
>>> import pygame
Note the lack of an error when importing it.
Credit to another answer dealing with the same problem on Windows.