Set up a Development -<--> Production git based system for a website

I want help in setting up a git based system where there would be a development server and a production server. We would work on our local machines and push to development, and once it works fine, we would push to the production server.
Reference: https://gist.github.com/cjsteel/5bdab49c97ecacb67904056ccdcb956d