Zakka Life, a very crafty blogger, has posted instructions for making this super-easy table decoration out of inexpensive black lace. She suggests that smaller versions could be made for placemats, too.
Her version is meant to be spread on top of the tablecloth, but you could also tack the web to a tablecloth with a needle and thread for a more permanent decoration. Then you wouldn’t have to worry about bumping the design and wrinkling it during dinner either.
It’d be cute to embroider little spiders on cloth napkins to go along with the tablecloth and placemats, too.