Because Eggbun is file-system based when it detects a .git folder it shows it in the sidebar's filetree. You can expand it to access the git hooks folder and edit those files or click on the .git folder to launch a git GUI.
To start the git GUI is quite simple. It currently:
We're still actively working on the git GUI. Soon you'll be able to do a lot more locally with git, customize your git email for different projects, integrate with GitHub and browse, clone, pull, push and everything else you're used to.
You don't need to have installed git on your system, Eggbun ships with its own git integration so you can just download Eggbun and get going.