Move the table to a workspace that is well-ventilated and has plenty of light. Place a dropcloth underneath the table.
Clean the table with a furniture cleaner to remove any old wax or polish, allowing you to get to the old finish more easily.
Strip the old finish, using an orbital sander. Run the sander over the surface of the table, allowing the sander to do the work. Don't press down too hard, as you may damage the wood. Continue sanding the table until the wood looks like new, with no signs of weathering. You can also use a chemical stripping agent. Generally, you'll apply a liberal amount of the stripping agent to the surface of the table and wait for it to soften the old finish. Scrape the old finish off with a plastic scraper with rounded corners, then wipe the table down with stripper wash to clean any remaining residue.
Sand the surface down to the bare wood with a sanding block, then wipe the table down with a tackcloth to remove any debris.
Apply teak oil to a dry rag and begin to cover the wood one section of the table at a time, applying the teak oil until the entire table has been covered.
Add a second coat of teak oil to the table after the first coat has dried.
Wipe the table down with a clean cloth to remove any excess oil. Allow the oil to set for about an hour.