Usually, just pushing the master branch to the github.io is enough. However, I use a webpage with some plug-ins that do not run on the github server. Hence, I build the website locally on a different branch and the push the built website to the master branch.
Step 1) Make sure you are on the source branch.
Clone this repository.
Checkout remote branch.
git checkout --track origin/source
Step 2) Build webpage and check that it works.
bundle exec jekyll serve
Step 3) Push your new webpage.
git branch -D master
git checkout -b master
git filter-branch --subdirectory-filter _site/ -f
git checkout source
git add _site/
git commit -m "Add compiled site." # this is optional.
git push --all origin