How can I have Github on my own server?
There is GitHub Enterprise to satisfy your needs. And there is an open source "clone" of Github Enterprise.
PS: Now Github provides unlimited private repositories, bitbucket does the same. you can give a try to both. There are several other solutions as well.
You have a lot of options to run your own git server,
Bitbucket ServerBitbucket Server is not free, but not costly. It costs you one time only(10$ as of now). Bitbucket is a nice option if you want a long-lasting solution.Gitea (https://gitea.io/en-us/)
Gitea it's an open-source project. It's cross-platform and lightweight. You can use it without any cost. originally forked from Gogs(http://gogs.io). It is lightweight code hosting solution written in Golang and released under the MIT license. It works on Windows, macOS, Linux, ARM and more.
Gogs (http://gogs.io)
Gogs is a self-hosted and open source project having around 32k stars on github. You can set up the Gogs at no cost.
GitLab (https://gitlab.com/)
GitLab is a free, open-source and a web-based Git-repository manager software. It has a wiki, issue tracking, and other features. The code was originally written in Ruby, with some parts later rewritten in Golang. GitLab Community Edition (CE) is an open-source end-to-end software development platform with built-in version control, issue tracking, code review, CI/CD, and more. Self-host GitLab CE on your own servers, in a container, or on a cloud provider.
GNU Savannah (https://savannah.gnu.org/)
GNU Savannah is free and open-source software from the Free Software Foundation. It currently offers CVS, GNU arch, Subversion, Git, Mercurial, Bazaar, mailing list, web hosting, file hosting, and bug tracking services. However, this software is not for new users. It takes a little time to setup and masters everything about it.
GitPrep (http://gitprep.yukikimoto.com/)
GitPrep is Github clone. you can install portable GitHub system into UNIX/Linux. You can create users and repositories without limitation. This is free software.
Kallithes (https://kallithea-scm.org/)
Kallithea, a member project of Software Freedom Conservancy, is a GPLv3'd, Free Software source code management system that supports two leading version control systems, Mercurial and Git, and has a web interface that is easy to use for users and admins. You can install Kallithea on your own server and host repositories for the version control system of your choice.
Tuleap (https://www.tuleap.org/)
Tuleap is a Software development & agile management All-in-one, 100% Open Source. You can install it on docker or CentOS server.
Phacility (https://www.phacility.com/)Phabricator is open source and you can download and install it locally on your own hardware for free. The open source install is a complete install with the full featureset.
I'm quite surprised nobody mentioned the open-source project gogs (http://gogs.io) or a derived fork of it called gitea (http://gitea.io) which basically offers the same what gitlab does, but with minimal system resources (low footprint), being perfect to run in a Raspberry Pi for example. Installation and maintenance is also way simpler.
Gitlab has made their service available to run on your own server for free. https://about.gitlab.com/downloads/