If you need to push your local git for the first time you should run the following (after creating the TFS 2013 git repository):
git remote add origin
http://tfs:8080/tfs/...
git push -u origin --all
If you need to commit a specific branch. You should publish this branch. See http://msdn.microsoft.com/en-us/library/jj190809.aspx#publish Until you publish the branch the commits on the branch will stay in "Unpublished branches"