If you have a Github account and would like to access it from Pythonista here's a script to download and install PyGithub: https://gist.github.com/4026453
It creates 'github' and 'dateutil' directories in Pythonista's Documents directory which you can import as modules. These aren't visible through the UI but can be seen for example by running @wrenoud's fantastic file browser (see http://omz-software.com/pythonista/forums/discussion/19).
An example use of the PyGithub module (which authenticates a Github user and lists the files in their public and private repositories) can be found here: https://gist.github.com/4051357
PyGithub provides a full implementation of the Github v3 API. For browsing operations the API is fairly self explanatory but for committing changes it is somewhat obfuscated (http://developer.github.com/v3/git/ is the best resource for help with understanding this). In principle, though, a fully featured Github client could be built on top of this implementation.
Some caveats:
1. I've patched the original PyGithub to use dateutil rather than strptime as I get errors the second time strptime is called (a quick google suggests that this is a fairly common problem). It's this patched version which is downloaded and installed, although you can try the original by reading the comments embedded in the script if you'd like. This is also the reason that dateutil is installed - the original PyGithub library has no dependency on it.
2. Beyond the simple example script I've not validated that all Github functionality works.