This wasn't too difficult to do for Ubuntu 15.04 and I assume the process for 14.04 would be the same. I first had to install zsh
sudo apt-get install zsh
and then restart my computer. I don't know why I had to restart but installing oh-my-zsh wouldn't work properly until I did. Then you need to make sure git is installed.
sudo apt-get install git
Once I restarted my computer I installed oh-my-zsh.