Docker containerization involves writing a Dockerfile that defines the environment for your Express app. The Dockerfile starts from a Node.js base image, sets a working directory, copies package files, installs dependencies, copies the app code, and sets the command to run the app. You build this Dockerfile into an image using 'docker build'. Then you run a container from this image, mapping the container's port 3000 to your computer's port 3000. This allows you to access the Express app in a browser or API client at localhost:3000. The container runs the app until you stop it. Key points include copying package.json before npm install to use caching, CMD sets the start command, and port mapping enables external access.