I don't think it's ever said how many there were, other than that there were more than one. The Galactica is often refered to as "the last Battlestar", though, so for the purposes of the show there's only one as far as anyone knows. However, in both the old show and the new one, there is at least one episode where another Battlestar shows up (the Pegasus); in the old show the Galactica and the Pegasus were the same ship with their nameplates changed, implying them all being the same class; in the new show (obviously) the Pegasus is a different class so there may be more. Hope that adequately sums that up
Oh, and there's no way the New Galactica could be a refit of the old show one. There's just too many structural differences. If they want to pretend to have a legacy then the old one would have been the namesake of the new, much the same way the Enterprise (Constitution class) became the namesake of the later versions.
