To hack Astrognome, you should get the recent GNOME libraries. Astrognome is using features of versions up to and including 3.10. Also, you should install SWE-Glib. It worths mentioning that SWE-GLib is sometimes evolves together with Astrognome: originally the two were in one project, but after a while I realised that SWE-GLib can be powerful in itself, so I split the project into two.
As of 30 July, 2014 Astrognome is developed using the GitHub flow. Basically, the main requirement is that everything in the master branch is working at any given time. If you have a new idea, create a separate branch for it, and if you think it is done, issue a pull request.
If, for any reason, you don’t like GitHub, you can still contribute. After cloning the repo, you can still create your own feature/bugfix branch, and send me a git-bundle or a simple patch (in which case you should mention the base you worked with) via e-mail.
If you don’t know how you can contribute, take a look at the TODO file or the issue list on GitHub.
Astrognome follows a well-defined coding style. If you contribute, please follow that by looking at existing sources, or use Uncrustify with the config file under docs/. The only thing it messes up currently is the alignment of object type #definitions and multiline variable definition blocks.