How do I stash uncommitted changes in Visual Studio 2013

In git the concept you're looking for is stash. You add your changes as if you are going to commit them, and you then stash them with git stash. After changing branches, you can git stash apply or git stash pop (with the former leaving the stash available for reuse).

I'm familiar with the shelf concept from Perforce, which has a useful difference from Git's stash -- where you can send a shelf to the server and share it with other people, you cannot do that with git. However, with git you can just create a branch with the stash and push that to the server, allowing others to merge it where it's needed.

Microsoft does not provide a way to use this feature.

Visual Studio 2013 Update 2 does not support shelving (called stashing in git) for git repositories, but you can use 3rd party tools on the repository itself (I use SourceTree).