You're probably getting near the end of the optimal season to do it. It's best to divide/transplant warm season grasses after they've started growing for the season, but before the foliage has reached ~18" high. That said, I've divided and transplanted them in mid-late summer, and although they sulked, and in some cases didn't bloom, they survived.

The best way to do it is with a very sharp and sturdy spade, like a nursery spade. Either dig out the whole clump and divide it, or dig out individual pieces of the clump. Sometimes, with an older clump, the center will be in the process of dying out. If that's the case with yours, take your divisions from the perimeter, cutting away the dying section.