Rub a clean, soft-bristled toothbrush into the furniture slots. When dirt comes out of the grooves, wipe it off with a clean cloth. Spray the grooves again, if necessary, to keep the area lubricated while you scrub with your toothbrush. Continue to go through all the slots in the furniture.
Removing accumulated dirt and grease from a table is a fairly simple, if tedious, solution. Grab a box of baking soda and some cheap vegetable oil, leave the fancy EVOO for another time. You'll also need a sponge or rag, a bowl, and a lot of patience. I hope this little cleaning tip will help you the next time you try to pick up the crumbs from your farm table.