In order to contribute to the Icinga Docs you are going to to submit a Pull Request on GitHub.
Here’s a little help on how to do that:
The workflow on GitHub is, that you make a “fork” (that’s like a clone of the repository on your account) and then you can create the pull request from there.
When you look at a project, you can usually just select a file over the GUI and use the web editor to make changes. This automatically generates you a fork if you don’t have write access. And from there you can also submit the Pull Request.
You can also have a look at GitHubs forking workflow guide.
When you got the process down, you’ve got your first steps done to contributing more to open source projects! 
How to contribute to the Icinga documentation on GitHub is described in the Contributing Documentation Guide on GitHub.
Thank you!