The best time to divide bearded Iris is July/ August. It's possible they're not blooming because they're crowded.. If it's another type of Iris, you might want to move the entire clump, and not disturb the roots too much . Herbaceous Iris (and other plants) are best divided in their dormant period. A picture paints a thousand words.. :) Helpful to know what area of the country you are in too.. Spring has sprung in California, but Boston is still under snow..

Thanks, Sherry. I'm in zone 3, high in the foothills above Denver. So the greens are only about 3 inches tall right now, as we've just come out of some snow....and will likely get more before all of this is over. I think they are bearded - the leaves are right - but never having seen them flower, I don't even know what color they are.....can't wait to see. The clump is about 6 feet by 6 feet, with many plants far too close together. It would make a nice border if divided up and spread out into good soil.

Wait til summer.. The rhizomes will be somewhat segmented.. You can cut off any segment that's behind the fan.. Spent sections usually have dried up, useless dead roots.. Just discard those.. They usually are just used up. I'm not sure what the recommendations for planting in Denver are, but where I am, we are told to plant the rhizome just barely below the surface.
Here's a good tutorial from the AIS:
http://www.irises.org/About_Irises/Cultural%20Information/Grow_Bearded.html

Thanks, Sherry!