To use GIT, it does not necessarily have to be with Github, there are other platforms that make Git available as a Version control, such as Bitbucket, Gitlab, Visual Studio Team Services.
As Renan said in another answer, you can use a number of other tools, as he himself quoted, Jenkins, Hudson, etc.
I know a lot about Visual Studio Team Services, and so my suggestion to you is to use this tool, by the following points:
It's Online, Free for 5 Developers and Unlimited Stackholders
You can create free unlimited repositories for your source code, either using TFVC or GIT;
You can manage your backlogs and integrate with your source code changes;
You can also have automated build processes, with validations of tests, architectures, quality, etc.
You can have automated Deployment processes as well.
You can create a Wiki for your project
These functions above, you can use for free in VSTS in the case with up to 5 developers.
You can also, by paying the part, have your nuget server and private npm.
Bacana, is that this works not only for Microsoft technologies, you can manage for example your Java project, automate builds, and Deployment of Java applications, including using linux servers for build and / or deployment target.
On learning git, there is a lot of good stuff on the internet, such as:
If you want to know more about VSTS, I have a playlist on my channel about it