EGit/JGit is a reimplementation of git in java, due to this GitHub does not officially support it. Issues have happened and repositories have been corrupted by them. While it is usually a simple matter to repair these repos due to git’s distributed nature, be aware that EGit may not work as well as the official git binaries.
GitHub officially supports msysgit (openssh) on windows and precompiled or self-compiled binaries on mac and linux. The following guide was submitted by a user and may be out of date.
Another description on how to use EGit and how to upload to Github can be found in the following EGit Tutorial