Can I use GIT with Visual Studio 2013 without using TFS?

Disclaimer: I am really new to Visual Studio. I know how to use and customize GIT, but not Visual Studio.

I need to work with a team on a project and we want to use GIT as a source control system. With GIT, what I would do is set up a remote repository on one of our servers and we will push and pull from the repository I created. However, when I try to connect Visual Studio 2013 with my created remote GIT repository, it gives me a series of errors. I have searched the web and everything that mentions Visual Studio 2013 with GIT seems to suggest that I am going to host my remote repository on Team Foundation Server, either hosted by my Microsoft, or configured on my own server.

The problem is that this project is on a rather tight budget, and the original programmer doesn't account for the cost of TFS. Is it possible to use Visual Studio's built in GIT functionality to work with a command, but without any TFS setup?

edit: My manager doesn't want to use any cloud hosting service, so I need to be able to keep a remote repository on one of my servers.