If you are interested in working with Docker I strongly recommend using Digital Ocean's hosting solution. They offer a 'Docker' plan; which means it already has all the required software and dependencies.
Otherwise, here are instructions for installing Docker on an Ubuntu 14.04 LTS server (which you can also get from Digital Ocean):
$ apt-get update
$ apt-get -y install docker.io
# fix paths
$ ln -sf /usr/bin/docker.io /usr/local/bin/docker
$ sed -i '$acomplete -F _docker docker' /etc/bash_completion.d/docker.io
# configure Docker to start when the server boots
$ update-rc.d docker.io defaults