My treatment for all woods is oil. Lemon oil, teak oil or just plain old mineral oil. Actually lemon and teak oil is just mineral oil with coloring and scent added. It nourishes the wood and prevents it drying out.

For your table, first I'd clean the surface of the table with mineral spirits and a soft cloth, to remove any dirt, grease or food. It will evaporate fairly quickly. Then polish and nourish the wood with a food grade mineral oil.
Food grade mineral oil is safe for any wood surface that will come in contact with food.

Thank you for your helpful response. I came here to ask the same question.

Thank you oilpainter for your response. Will the mineral water be enough to pull up the grease stains (i.e toddler paw prints? Thank you again.

Wouldn't mineral oil be ineffective on wood that has a urethane finish? And isn't it likely that a piece of furniture with a veneer top would have such a coating?

I would pour some mineral spirits on a rag (buy the odorless type), and wipe the table with that.

kjbal, just to clarify: posters are recommending mineral "spirits" not mineral water. You can buy this at any good paint store or hardware store.

Here is a link that might be useful: mineral spritis