Building a forge requires lining an appropriate material with furnace cement to hold the burning coal and a hood and vent to remove smoke. By using two sinks for the main part of the forge, you can create the quench tank you need to cool metal next to the forge's burning chamber.
Popular Mechanics outlines a plan for a forge that uses two sinks as the basis for the forge. One of the sinks holds water to serve as a quench tank, while the other is lined with furnace cement to safely burn the coal. Ensure that the cement layer fully covers any surface coal it might come into contact with to avoid melting the metal that holds it.
Burning coal creates potentially dangerous smoke, so it's important to use a hood to capture this smoke. In order to dissipate smoke safely, attach a stovepipe to the top of the vent. Longer stovepipes ensure that the smoke doesn't waft back down if there's a light breeze. To make sure the coal stays hot, you need to actively blow air into the burning chamber. A vacuum cleaner with a hose attachment works well if it can be set to blow air, and attaching a valve lets you find the right airflow for your system.