According to documentation installation process of docker on Ubuntu/Debian based OS's is pretty easy. We can install it with apt-get:

sudo apt-get update && apt-get install docker.io

After that we can just pull some image from repo and play with it. For example

docker pull ubuntu

or if you want only last ubuntu version

docker pull ubuntu:14.04

We can check downloaded images with

docker images

Result will be like:

root@atom:~# docker images
REPOSITORY          TAG                 IMAGE ID            CREATED             VIRTUAL SIZE
ubuntu              14.04               2d24f826cb16        3 days ago          188.3 MB

And after that we can create some ubuntu container with

docker run -i -t ubuntu /bin/bash