Tablecloths are bound to get stained. One solution is to forgo them entirely, using a well-sealed wood or laminate tabletop instead.
Scrape off as much as possible with a kitchen knife or spoon. Spread over a pad of paper tissues or cloths. Rub the stain with a toothbrush dipped in eucalyptus or Orange Power. Replace the paper tissues or clothes as they become stained. Dried tar: Soften with warm olive oil, then repeat the above procedure.
If the fabric can withstand hot or boiling water, spread the stain out over the sink, covering it with borax. Pour boiling water over the stain, then let sit in the water until it cools. Another technique for removing tea stains is to rub lemon juice into the stains, then hang the item in the sunlight.