Do I need a tablecloth or placemats?
If the table itself looks great and you don't want to hide it - use place mats rather than a tablecloth, just as you might go for an area rug to make your living room cozier but still show off the hardwood floors.
On the other hand, if you want to cover your table entirely, use a pretty tablecloth as if you would use wall-to-wall carpeting to cover an unfinished floor. You should have some neutral tablecloths on hand, such as pale linen. For more festive occasions, go with colorful table linens or placemats to bring the party to life and reflect the theme and food.
What's a runner for?
A runner - a long, narrow piece of fabric that is usually centered down a rectangle, table length wise - is a great way to dress up your table without being too formal. If you are serving dinner family style, bowls and platters should be placed on the runner with place settings on either side.
While it is nice to show off a beautiful wood or marble table by leaving some of it uncovered, a runner can also be layered over a tablecloth. Be sure both fabrics are smooth and not too thick, or you'll create a lumpy area for your dishes and platters to sit on. If your table is relatively wide, you can use runners as extending placemats that run down the length of the table, leaving the middle exposed. A more modern treatment is to place two or more short runners across the width of the table, so they sit under the place setting in pairs and connect people who are seated across from each other.
For more on table settings and seating, check out these tips on how to facilitate the art of conversation at your dinner.