If you are invited to work on a GitHub repository and you want to do so from Visual Studio 2013, then you can follow these steps:
Get the URL to the GitHub repository
Go to the repository on GitHub.com and copy the HTTPS clone URL or click on the copy to clipboard button:
Open Microsoft Visual Studio 2013.
Open the Team Explorer.
Click on the Clone button under "Local Git Repositries"
Enter the "clone url" from the GitHub page and enter a local folder, to store the code.
Open the code cloned and your good to go.