We have a computer on our local network designated as \'the server\', that runs Windows XP, where we keep the shared folders and stuff that should be visible to all.
How
Edit: I recently found about Bonobo Git Server - it is a free and open-source Git Server for Windows and IIS, licensed with an MIT license. I haven't tested it myself yet, but you can give it a try.
There is also this CodeProject article - Step by Step Setup Git Server on Windows with CopSSH + msysGit and Integrate Git with Visual Studio
Old answer: In the end, I did as @meagar suggested - I created a shared folder on the server, and I followed this tutorial, the part about using Git Gui. Note that we use pushd/popd because CD does not support UNC paths:
pushd \\remote-pc\SharedDocs\MyRemoteGitRepo1
git init --bare
popd
Now all you need to do is connect your local repo to remote one. Note that you need to use forward slashes for git remote add origin, or it won't work:
cd C:\Workspace\MyLocalGitRepo1
git remote add origin //remote-pc/SharedDocs/MyRemoteGitRepo1
And finally you can push your work to the remote repo:
git push origin master