The specifics depend on your field, and I think most areas have very loose guidelines as to what to do in these situations. The only hard-and-fast rule is that you need to get it past your reviewers and your editors, who will tell you if the style is inappropriate. Other than that, the most important thing is that you yourself are happy that the citation is getting your GitHub repo the most visibility possible. Finally, you should consider your paper from the perspective of readers that may want to use and cite your code, and who will naturally look to your writing for how to do that.
In general, I would recommend citing the code in the bibliography, as one more reference. The advantage of this is that your article's references will be listed and indexed separately, and (with luck) this will register as links pointing towards your repo, which will become more of an advantage if more people cite it. Such a citation should have
- the name of the programme,
- the URL of the repository, and
- a clear indication of the version cited and its date.
An example citation is
G. A. Worth, M. H. Beck, A. Jackle, and H.-D. Meyer. The MCTDH Package, Version 8.2, (2000), University of Heidelberg, Heidelberg, Germany. H.-D. Meyer, Version 8.3 (2002), Version 8.4 (2007). See http://mctdh.uni-hd.de
You should also describe the code within the text when you first cite the code, and provide a complete enough description within the paper that readers do not need to go read any additional information to continue reading your paper, because it needs to read like a single, coherent piece of work.
Alternatively, you can cite it in a footnote, indicating the name of the code and its location. This would be a good place to include the description if it is brief. Another choice is to do this in the acknowledgements, as giordano points out. However, I think these make your code less discoverable to both humans and search engines.
As I mentioned before, you should mould your citation of the code in the way that you'd like others to cite it. It is also desirable that you include, within the pages describing code online, a description of how you want people to cite the code. Some examples are GAMESS UK, MCTDH and MOLCAS, or the ones in this question. Having such a description will strengthen your position should referees or editors not like your preferred style. You set the terms on which your code gets cited!
Finally, as others have mentioned, you should make sure that the URL you point to is stable, as you will be unable to change the link in the published paper once it goes out. This is a separate question altogether, and there are a number of ways to do this - including supplementary information to the article itself, separate repositories for academic code, and of course GitHub itself - and you should strive for the most stable solution possible. Is it likely that the repository will someday get closed or moved? If so, you should consider alternatives.