Run commands using docker container

I'm currently working on a plugin for PhpStorm. It adds a section to the project generation wizard using directoryProjectGenerator extension point. from there I want to execute some commands inside a Docker container to create a new project following these steps:

1. pulling an image if not exists,
2. run some command using that image
3. attach a progress indicator to the running process inside container

I already added Docker plugin as a dependency, but I'm not sure which classes should I use.

What is the proper way to do that?

Thanks in advance.