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.