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Modern Starfish
Starfish comprise the class Asteroidea, within the phylum Echinodermata. A class is a fairly high-level taxonomic grouping -- all mammals, for example, constitute the class Mammalia -- so to ask about the ancestors of the starfish is to probe back into the distant evolutionary past. There are seven orders of starfish, each of which includes several families, and ultimately about 1,600 different species in total living today. The earliest asteroid fossils date from the Ordovician period, between 490 and 443 million years ago.
Brittle Stars and Basket Stars
In addition to the true sea stars of the class Asteroidea, there are also about 1,600 species of brittle stars and basket stars belonging to the separate class Ophiuroidea. They resemble starfish in many ways, but are different enough that biologists do not consider them to be of the same class. Even so, they are thought to have a common ancestor with the asteroids which would have lived some time before the Ordovician. This animal would have resembled both brittle stars and sea stars, but would of course be a distinct kind of creature from anything alive today.
Echinoderms
The asteroids and ophiuroids, together with a now extinct class called Somasteroidea, are all Asterozoa, descendants of a branch of echinoderms which must have still looked vaguely like a starfish in that it would have had radial arms. The other branch of echinoderms, the Echinozoa, contains the sea urchins, sand dollars and cucumbers, which also show radial symmetry. It's therefore almost certain that the latest common ancestor of the echinoderms was radially symmetrical, probably five-fold, but it's hard to be sure what it would have looked like. It must have lived at least as long ago as the mid Cambrian, or 543 to 490 million years ago, and possibly as early as the Vendian.
Deuterostomia
The echinoderms are all descended from an ancestor that also gave rise to the phylum Chordata, which includes vertebrates and therefore humans. The group that includes these two apparently very different phyla is called Deuterostomia, which means "mouth second" and has to do with the embryological development of these creatures. The ancestor of all deuterostomes must have lived some time before the Cambrian, and while it is hard to imagine just what it looked like, it probably had a segmented worm-like body rather than radial symmetry. Imagine a five-segmented worm biting its tail, and then growing out in that position, and perhaps that is how the echinoderms became radial.
Bilateria and Beyond
If the most recent common ancestor of man and the echinoderms was a segmented worm-like creature, then it was bilaterally symmetrical, in that it had a right side and a left side. Its own ancestors included the ancestor of Bilateria, all bilaterally-symmetrical animals, from lobsters to squid to mosquitoes. Again, it is difficult to know what it looked like beyond some kind of worm, but its ancestors were the ancestors of all animals, likely beginning as single-celled eukaryotes, hunting and eating single-celled algae.