Place a white T-shirt or white cotton towel on top of the white spots or rings, doubling up the shirt or towel.
Pour water in the steam iron reservoir and set the steam iron to a low heat setting, lower than the cotton setting.
Iron on top of the T-shirt or towel you placed over the spots. Keep the iron moving rather than sitting still over the spots.
Check the spots each time you run the iron across them and wipe up any excess moisture you make. It may take several swipes with the iron, but soon you will notice the white spots beginning to disappear.
Wait about 30 minutes or so after the white spots or ring removal, then apply a little furniture polish with a soft cloth to your kitchen table. This restores the dull surface the table may have acquired with the iron treatment.