Automating builds of docker containers on hub.docker.com is a fairly straightforward process, assuming you have a repository on GitHub containing a Docker file.
Here is an example repository.
First, on Docker Hub, choose the "Create" drop-down and select "Create an Automated Build".
If you haven't linked a GitHub or BitBucket account yet, you will be prompted to do so. Select "Link Accounts" and follow the prompts.
Select "Create an Automated Build with < Provider >".
From there, it's simply a matter of selecting your repository containing a Docker file.
Once the automated build is setup, pulling the container is as simple as executing a docker pull