Building TimescaleDB on Docker involves several steps that can be simplified with the right guidance. To start, one needs to have Docker installed and set up on their machine. Then, a new container is created using a Docker image such as Ubuntu, which serves as the base for the TimescaleDB system. The container is then configured with necessary packages, including PostgreSQL, and the TimescaleDB repository is cloned from GitHub. The build process involves preparing the build system, building the extension, installing it, and setting up the PostgreSQL instance with TimescaleDB. This includes configuring the PostgreSQL configuration files, editing the "pg_hba.conf" file, and adding the TimescaleDB extension to the database. Finally, a Dockerfile can be created to automate the setup process, making it easier to spin up a TimescaleDB instance. By following these steps, users can build and run TimescaleDB on their machine, either for testing purposes or to contribute to the open-source codebase.