We keep our in a small basket on the table, just like we did with the paper napkins before and where they can be easily gotten to when I set the table. I wash them with our towels and they actually enjoyable to fold, but I've always enjoyed folding towels (though I can't say the same for the rest of the clothes.) We also tend to use one napkin for all three meals as they just don't get "dirty" very quickly, but that also depends on what we are having. Fried chicken usually means for a messy napkin by the end of the meal. :o)
They also have many other uses. I have covered up leftovers in the fridge with them instead of using plastic wrap or foil. I have used them to play peek-a-boo with a baby at the dinner table to keep her entertained for just a few more minutes while Mommy finishes her meal. I have used them as a baby head scarf in play. They work great for wrapping up things to go into a picnic basket (cookies, bread, a sharp knife, hot sandwiches wrapped in foil then in a napkin to keep them warm, ect.)
Cloth napkins are frugal in that you don't keep buying and throwing away paper ones. Just imagine yourself throwing away a penny or two every time you toss out a cloth napkin.