FIRST, commit changes to the website source in master.
THEN, in the repository root:
git checkout master
cd site
jekyll build
cd ..
git checkout gh-pages
cp -rf site/_site/* .
git add .
git commit . -m "updated site"
git push
git checkout master
Start the server:
jekyll --server
jekyll --server --auto # recompiles html files after changes
Browse to:
http://0.0.0.0:4000