Almost all versions of Linux ship with a recent enough version of Python, so it is unlikely that you will need to install Python yourself.
On Ubuntu, most of the pre-reqs are available in the Ubuntu software repos and can be installed using apt-get:
sudo apt-get install python-qt4
sudo apt-get install git-core
sudo apt-get python-numpy
sudo apt-get python-scipy
sudo apt-get python-matplotlib
sudo apt-get update
Now we shall install pip.
Most Python distributions ship with a tool called easy_install which assists with installing Python packages.
Although easy_install is capable of installing most of the dependencies needed for SunPy itself, a more powerful tool called pip provides a more flexible installation (including support for uninstalling, upgrading, and installing from remote sources such as GitHub) and should be used instead.
Use easy_install to install pip:
sudo easy_install pip
You are now ready to install SunPy and its dependencies.