Currently I'm developing some applications that I want to share with the community. Therefore I decided to use github. I could find a lot of tutorials that tell me how to create a repository from scratch in github, but I couldn't find one that tells me how I can share an existing eclipse project. I would prefer a solution that works inside eclipse using a GUI.
You can follow this user guide section of git push (to a GitHub repo), adding a remote with the ssh address of your GitHub repo:
See also this tutorial to push your local project to that GitHub repo.