To build a GPU accelerated Docker container with TensorFlow or PyTorch in it, you can follow the steps outlined in this tutorial. First, install Lambda Stack on your Ubuntu host system, followed by installing Docker and nvidia-container-toolkit. Next, build an open source Lambda Stack Dockerfile to create a custom image, ensuring its creation by running `sudo docker image list`. You then run a test job within the container using the `docker run` command. Finally, upload your container image to a registry, such as Docker Hub, and verify it works on any new computer after installation. With these steps, you can now use Lambda Stack + Lambda Stack Dockerfiles for GPU accelerated deep learning containers.