Here is a step-by-step tutorial on how to polish a stainless steel sink:

1. Rinse the sink with faucet water and coat it with baking soda.
2. Scrub the sink in the direction of the steel grain with a soft cloth or a fine grade of steel wool.
3. Spray on undiluted vinegar, wait for a few minutes, then rinse the sink.
4. If necessary, apply a paste of vinegar and cream of tartar to remove any stains, then rinse again.
5. Buff the sink with a few drops of olive oil or club soda to restore the shine and smooth out any scratches.