James Wade has posted a tutorial to his site showing you how to combine Docker and WordPress after some experimentation of his own.

I’ve been meaning to get started with Docker since hearing about it in 2014. Having really enjoyed working with Vagrant, I’ve struggled to make a leap into the Docker realm. [...] My understanding at the moment is that docker takes up less resources, which for me is becoming more and more of an issue as I attempt to expand my development environments. Also, I’ve recently inherited a number of Vagrants that I discovered have varying operating systems and application versions, that vary from production.

This has unravelled a dependency hell when I came to build a continuous integration process. In light of this, at this stage, a complete rewrite of the architecture seems to be emerging as the most sensible way to being all the services in to line. I’ll be looking whether I can solve these problems (amongst others) with Docker.

He starts by helping you get all the tools you'll need installed with examples for multiple platforms (OSX, Windows, Unix-based). With those in place he helps you set up a VM as a Docker machine then get WordPress installed (complete with its database). He also shows how to use Docker Compose, using an existing WordPress instance and creating a custom image from the results (including database, environmental settings and hostname configuration).