Siberians are quite easy to divide, and it can be done either in the spring or fall. You're in a warmer zone so I'd recommend doing it now giving the new divisions a chance to settle in before cold weather. They can be divided in two ways: dig up the whole clump (the rhizomes and stubby roots are fairly shallow and come up easily) and cut the clump into wedges with a sharp knife. Or simply plunge a shovel in to remove a chunk. If the crown of yours is about two feet across (is it growing in a ring with a bare spot in the middle... sort of like a doughnut?) I'd simply shovel divide it into several pieces. Just make sure not to make the pieces too small; probably wise to get eight to ten fans per division. That way you've got a good sized plant with plenty of rhizome/root attached. Water well after replanting. The main thing is not to let the roots dry out. Don't be afraid to just go ahead and do it, Siberians are pretty tough. I would think that all of the divisions would bloom for you next season if you do the dividing now. If you wait till spring, they probably wouldn't bloom until the following season.

Probably the lack of information is due to the easiness of the project. As was stated just take a shovel and quarter it up. You should get bloom from 2 or more of your divisions. I had to move everyone of my siberians in the middle of the winter last year and they all bloomed. I also live in zone 7.