What do you mean by "git server"?
git server exposed to the internet
means
- web-git interface, therefore it also implies http server, running PHP/Python mod + PHP/Python programs
- SSHd, exposed to the internet
- (optionally) GITd exposed to the internet
- high security policies (1)
- a system to collect { requests, notes, comments, bugs reports, ... } usually using a PHP/Python mod (2)
- a way to provide and manage pull requests (3)
(1) if you expose on the internet, you have to pay much more attention, and they are things that with distros like Gentoo you don't find already set up, you necessarily have to review carefully and in every single detail, so say "I'll make a git server" that only runs in your own infranet and never goes on the public internet, it makes a huge difference also in how to compile and configure each single dependency.
(2) git itself only allows you associate your email with your commits, which is nice, but then you still need something to public interesting comments, notes, and various bug issues.
(3) "pull request" is not features of Git itself, it's a feature offered by Github. So, you need to provide a similar mechanism!
This, because usually, you do not have permission to clone and push someone else's repository on the internet, so you "fork" it into your own Github repository
Then you can clone your own Github repository and push your commits there
If you want your commits to go into the original author's repository, you first define another origin for that repository - called "upstream" - and then you send a "pull request"