This guide will go over installing the git plugin for Jenkins. It assumes you have Jenkins already installed and running (Very basic setup). If you have not done that yet I wrote a how to guide at http://www.whiteboardcoder.com/2014/01/install-jenkins-ubuntu.html
As a side note there is a github plugin to Jenkins https://wiki.jenkins-ci.org/display/JENKINS/GitHub+Plugin  But I will not be going over that, rather I will just use the basic git plug-in to talk to github
Install git via apt-git
First git needs to be installed on the Ubuntu machine
> sudo apt-get install git
Install plug in
Open your Jenkins install in a web browser. Mine happens to be located at http://192.168.0.7:8080/
After you login click on Manage Jenkins
Click on Manage Plugins
Click on the Available Tab
In the filter enter "git plugin"
Then select "Git Plugin" and finally click on "Install without restart"
Plug-in installation starts
After the plug-in is successfully installed click on "Go back to the top page"
Create the ssh keys in the Jenkins home directory. In my set up the Jenkins home directory is at /var/lib/jenkins
Switch over to the Jenkins user and create its ssh keys
> sudo su jenkins
> ssh-keygen -t rsa -b 2048
Copy the id_rsa.pub key to obtain it you could run the following command
> cat .ssh/id_rsa.pub
Copy this somewhere in order to upload it to github
Upload ssh keys to github
Login to github.
From your profile click on SSH Keys
Click on Add SSH key
Give it a Title, Paste the id_rsa.pub text into the key and click Add Key
Open github repository
Click on New Job
Name it Test
Select "Build a free-style software project"
At this point you need to get the url of a remote git repository to clone from.
For this example I chose jquery https://github.com/jquery/jquery 
The URL to clone is located here on their github page, copy it.
In this case its
Replace the : with a / to give you and prefix it with ssh://
Now back to the Jenkins job page
Select "Git" then enter the github remote repository
Click Build now
The Build was successful
This is a very simple deploy, all it does is download from the github repository.
This same technique works with closed github projects your github user has access to.
 Jenkins github plugin
 jquery github site