Cover your work area with a dropcloth and place the table in the center of it. The dropcloth will help gather the sanding dust and debris, limiting the cleanup and protecting the area.
Prepare your sander by attaching a new sanding disc. Refinishing teak requires a lot of sanding, so you'll need the new disc for best results. Sand the table in a back-and-forth motion with smooth strokes. Use a sanding block to cover uneven areas or tight spaces that may be missed by the orbital sander. Continue sanding the table until the surface has lost the gray tone and weathered appearance, uncovering the raw wood underneath.
Wipe the table down with a slightly dampened rag to clean up all of the sanding dust. It is important to limit the amount of water and dampness the table is exposed to, as the raw wood is unprotected and can be damaged if it gets wet.
Apply teak oil to the table in small sections, using a soft cloth. Wear gloves when doing this part. Cover the entire table, and then apply another coat in the same manner. Repeat this process until your table no longer absorbs the oil.
Wipe the table down one last time with a clean, dry cloth after applying the last coat of teak oil. This will clean up any teak oil that was not absorbed. Allow the table to sit for one to two hours, or until dry, before using it.