Prerequisits

Install Git
Install Ruby
Install Jekyll and Bundler

$ gem install jekyll bundler

GitHub

Create a GitHub-account
Create a repository on GitHub
(It has to be public if you use GitHub Free, note that your code will be visible to everyone!)

Local Repository

Clone the repository to a local directory:
SSH

$ git clone --recursive SSH_URL

HTTPS

$ git -c http.sslVerify=false clone --recursive HTTPS_URL

Directories

Create two directories: docs and localDev.

$ mkdir docs $ mkdir localDev

docs will contain the content of the website later on.
localDev will contain our Jekyll project.

Create Jekyll Project

Move to the localDev-directory:

$ cd localDev

Create a new Jekyll-project at localDev-directory:

$ jekyll new --skip-bundle .

(make sure you got the dot)
Open the Gemfile that Jekyll created and comment out the line which starts with gem "jekyll"
Add the github-pages gem by editing the line starting with # gem "github-pages".
Change this line (# gem "github-pages") to:
gem "github-pages", "~> GITHUB-PAGES-VERSION", group: :jekyll_plugins
You can find the actual version of GitHub-pages here
. Now save and close the Gemfile.

Now still being at the localDev-directory, install the bundle:

$ bundle install

Optionally you can make changes at the _config.yml file.

Learn Jekyll

Follow this guide to learn Jekyll. Make sure that all files and directories you create are in the localDev-directory.
Note that building locally will not work according to commenting out gem "Jekyll" at the Gemfile. (Atm I didn't check if this is right)

Build Project

After creating all necessary files and dirs, you can make a production build:
Note that all files at _site will be cleared!

$ JEKYLL_ENV=production bundle exec jekyll build

Your Jekyll-project was now build and stored at _site.
Now move the content of the localDev/_site to docs:

$ cp -r _site/* ../docs

And push your changes to your central GitHub-Repository.

Publish Website

Now publish your repository on GitHub Pages.
Select your branch and as folder /docs and hit Save.
Now you have to wait, this can take up to 10 minutes.
On the top of the page a box will appear with the url of your website.