1. Go to the GitHub website
2. Open your repository
3. Click Settings
4. Under GitHub Pages, click "Launch Automatic Page Generator"
5. Follow the instructions

1. Create a new repository or clone an existing one.
2. Create a new branch called gh-pages without any history

$ git checkout --orphan gh-pages

# ensure you are in the correct directory then,
# remove all files from the old working tree
$ git rm -rf

3. Add an index.html file to the root of the repository.

$ echo "Hello World" > index.html
$ git add index.html
$ git commit -a -m "First pages commit"

4. Push to Github.

$ git push origin gh-pages

You can now load your new Github Pages site at http(s)://<username>.github.io/<projectname>

You will need a domain name from a registrar.

In the gh-pages branch of your project repository, or the main branch of your username.github.io repository, create a CNAME file with the contents www.yourdomain.com - the canonical domain.

At your registrar's domain configuration page, point your domain to your GitHub website. Set up two CNAME records (one for the root apex (@) and one for www). Both should point to username.github.io or username.github.io/repository. If your DNS provider does NOT support ALIAS records on the root apex (@), simply create A records that point to 192.30.252.153 and 192.30.252.154.

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Resources

GitHub instructions for a custom domain

Stack Overflow Q&A: "Custom domain for GitHub project pages"

Audrey Watters - Using GitHub to Power A Web Project: How and Why

Alex Cican - How I moved my websites to Dropbox and GitHub

Treehouse - Using GitHub Pages To Host Your Website