If you have set up a directory with generated HTML based on the gist below, you may do the following from the /docs directory to publish to Gihub pages:
make html
cd build/html # or your build directory depending on config
git commit -a -m 'made some changes, yo'
git push origin gh-pages
The full gist to setup the publishing of HTML pages generated with Sphinx to Github pages (originally by @brantfaircloth):