Clear the top of your dining room of any clutter that may be sitting on it.
Plug the clothes iron into an electrical outlet near your dining room table. Allow it to heat until warm, but not hot, before moving onto the next step.
Lay the large square of linen cloth flat on the table top.
Test a small area of the cloth with the clothes iron. Iron the cloth, allowing for several sweeps and passes with the iron. Check underneath the linen cloth. Notice the cloudy buildup condition. If it is lessening and there is no damage to the surface of the wood, continue ironing the linen cloth on top of the wood until you have covered the entire surface of the dining room table.
Follow up with a light polish, or other wood furniture conditioner as desired.