TIL that IntelliJ has a Docker plugin that gives you a UI tool within the IDE to integrate with Docker (running on your local machine). Not much different from integration with other servers like WebSphere, Tomcat and so on.

Step 1: install the Plugin

Basic set-up is easy. Just point to Docker.

Step 2: Map Ports etc.
Clicking on the same two arrows, but then selecting the "Edit Dockerfile" option allows you to map ports and to specify other options you might otherwise need to provide at the Docker command line.

Step 3: Run your Dockerfile
Once this is done, when you open your Dockerfile, you will see the typical green "Run" arrowheads in IntelliJ (or whatever shows in your theme).

Step 4: Monitor and Control
The "Services" tool tab allows you to monitor the container's logs, and to control various other aspects... check out the various tabs.. For instance, you can look at the environment variables.
It also has an option to run a docker exec So, it's easy to jump into a shell in your container to check it out.