Trouble running local jekyll server for the docs folder of a private project

I have private project with the documentation sitting in the docs folder.
And the project repro is connected to the local repro folder on my PC.
But I am getting tired of updating the local .md files, pushing the changes and waiting till github republishes the changed content to github.io.
So I would like to run a local jekyll server using my local docs folder (of course using the same theme as the final github pages site)

I have been unable to find doc that particulary covers this case.
So if anybody can point in the right direction that would be very much appreciated.

GitHub Pages is built on Jekyll, a static site generator written in Ruby. You can follow these instructions (except for the part about generating a new Jekyll site, of course) to get it running on your system and use the jekyll serve command to serve the site locally. You may also need to install the gem for whatever theme your Pages site is using.

I hope that helps!