To run Django-Neomodel within a Docker container, one needs an updated version of Docker and Django Neomodel installed. The process involves creating a Dockerfile that collects the commands to create the environment, a docker-compose.yml file that configures the ports for communication with the Neo4j database, and a docker-entrypoint.sh script that configures the python/Django portion of the app. Once these are in place, running `docker-compose up` starts the container and allows access to the Django admin and Neo4j browser at specific URLs. The environment variables and commands in the Dockerfile and docker-entrypoint.sh script configure the installation of dependencies and creation of superusers for the Django application. This setup is useful for empowering app development for developers, especially those working with Neo4j and Django.