The best time to divide and transplant irises is after they flower (late summer or early fall) while the plants are dormant.   This should be done 4-6 weeks prior to the hard frost.  For bearded irises, July or August is idea, while Siberian irises can be divided in early spring or late summer.  

1)  Cut back foliage.  Trim leaves to 4-6 inches for Siberian irises.  

2)  Remove any remaining flowers.  Cut stalks close to the leaves to reduce stress on the plant.

3)  Loosen the top 2-3 inches of soil.  Do this with dry soil for easier lifting. 

4)  Using a spade or fork, insert the tool 6-8 inches from the leaves to avoid damaging the root and gently lift the clump.

5)  Clean the rhizomes, rinsing soil from roots to inspect them.  

6)  Select healthy rhizomes (they should be firm with several roots and a fan of leaves). 

7)  Cut the rhizomes using a sharp knife to separate them into individual divisions.

8)  To replant, dig a hole large enough for the rhizome and roots that gets 6-8 hours of sun.   Build a small mount in the center.

9)  Position the rhizome on top of the mount, spreading the roots around the mount.  Ensure the rhizome is just at or slightly below the soil surface, pointing the leaves away from other irises so they don't crowd each other.

10)  Cover and water, filling the hole with soil and water thoroughly.  Mulch lightly if needed.  

The transplanted irises may bloom sparsely the following spring but should reach full bloom by the second year.  Soil should be moist, but should drain well.  

Here is a YouTube video that may be helpful: