I\'ve already set up a Git repository on GitHub and committed a few changes from my Windows machine.
But tomorrow I\'ll have to work in this repository from a machin
I don't like link-only answers, but this link I followed step-by-step on a Fedora machine and it worked without modification.  Very, very easy.  The binaries end up in your ~/bin directory.  You download a tarball, extract the sources, run make and run make install and that is it.
As the author states, the 2 prerequisites are gcc and ssh and if you meet these git should work for you as a non-root user.