Clear everything off the tables and dust each table with a feather duster.
Put on dishwashing gloves and wipe down each teak dining table with wood oil soap, using clean cloths. This cleans the surfaces sufficiently to prepare them for refinishing.
Dampen another cloth with mineral spirits and wipe away the wood oil soap residue on each table. Let the wood air dry, leaving the mineral spirits to dissipate.
Sand each table in its entirety, going in the same direction as the wood grain, using ultra-fine sandpaper.
Wipe away the sawdust with a tack cloth. Gently rub each teak dining table with steel wool to complete the sanding, and then wipe again with a tack cloth.
Sponge on wood oil. Use teak oil or a finish that matches the original color of the dining tables. Apply with the direction of the wood grain and allow to dry for at least 30 minutes.
Apply a second application of teak or wood oil finish with steel wool to work the finish deep into the wood grain.
Lightly dampen ultra-fine sandpaper and sand the second coat of finish gently, going in the direction of the wood grain. Then apply a third coat of wood oil finish with a sponge.
Let the third application dry, and then buff each teak dining table with a microfiber cloth.