Just clip off the spent bloom (or the end of the flower stalk that is left when the petals fall) with a scissors or pruner if you can't snap it off by hand. The star like remainder is the seed head. They won't bloom again.

Normally, it takes 3-5 years to grow a peony from seed. So much simpler to buy a blooming sized plant or to try your hand with some inexpensive bare root stock available just about anywhere plants are sold. I bought some packaged bare roots from Wal-mart late this March. Right now they're healthy, good sized plants. They aren't likely to bloom this year, but should by next year.

If you want your bushes to look tidier, follow the flowering stem down to the leaves and cut just above the leaf about 1/2-1/4 inch above. If you cut closer that leaf may discolor and need to be removed.