The family has gone home. The leftover turkey carcass is safely ensconced in the fridge, waiting for 2:00 a.m. picking to commence. Now, you have the heavily soiled tablecloth with which to contend. How do you clean it? Well, that depends on the material from which it's made. If the tablecloth is vinyl, all you'll need is some spray cleaner, a sponge, and some paper towels. Tablecloths are made from other materials, too, such as cotton, silk, and linen. Each requires a different cleaning method, as follows:
You can clean cotton tablecloths in the washer and dryer. Wash them in a cool-water cycle. Don't use bleach unless absolutely necessary, and make sure it's colorfast (oxygen) bleach if the tablecloth isn't white. Run the dryer on low heat and remember to remove the cotton tablecloth as soon as the cycle finishes.
Silk tablecloths have the same properties as other "delicates." Unless they are so heavily soiled that hand washing would be ineffective, you should wash them by hand. Do not use high-powered detergent; use a mild cleaner instead. Shampoo works very well if the tablecloth isn't badly soiled. If hand washing doesn't work, wash on the gentle cycle in cold water. For best results, wash a silk tablecloth in an "in-the-washing-machine bag." If you use the washing machine, use a detergent specifically for delicates. Line dry silk, if possible, or use the "fluff" setting on the dryer, which uses no actual heat.
Linens should be treated with an oxygen-based bleach prior to washing. Never use chlorine bleach on linens. The chlorine will react with the flaxen fibers and create a yellow color instead of linen's usual pure white. After treating with an oxygen-based colorfast bleach, wash normally in the gentle cycle. If the stains are stubborn and won't come out, you can treat them with an enzyme-based cleaner, such as Shout®. Never put linen in the dryer. Hang it on the line instead. Not only will this make the tablecloth smell fresh, but it will also prevent slight burning stains from the dryer.
If you're not comfortable doing your own tablecloth cleaning after Thanksgiving, then a professional cleaning service would be able to do the job.