Bearded irises can be divided any time after your last frost date in the spring, but many irisarians believe the optimal time to divide them is 6-8 weeks after bloom. Avoid transplanting irises in very hot weather (90+ F degrees), but do get them transplanted back into the ground a couple months before freezing weather to give them time to root in well before winter. Irises sometimes take a year off bloom after transplantation to settle into their new homes, so don't be too disappointed if you don't get bloom the spring after planting. Irises moved before bloom will often lose their bloom that season as well, which is why it's best to wait until after bloom to dig and divide.
Use a spade or fork to dig up your iris clumps and wash them off well with a hose until you have removed all dirt and can easily see where the rhizomes (rzs) are attached to one another. With a sharp knife, cut through the attachments (you can break them apart with your hands, but a sharp knife will make a smaller, cleaner wound). Inspect the rzs thoroughly. Discard any rhizomes that are soft or mushy or show any other signs of disease, any that do not have viable roots, and any that are just too tiny to bother with. Many people also discard old "mother" rhizomes that have already bloomed because they will not bloom again. These "mothers" may grow additional rhizomes (increases) however, so they may be worth replanting if you have the extra room for them. Remove any dead, spotted, or unhealthy (brown or yellow) leaves or parts of leaves. Many folks cut the leaf fan back a bit when transplanting so the weight of the leaves won't cause the newly planted iris to tip over, but you should leave as much leaf on the plant as possible to continue to feed the rhizome. Snap or cut spent bloomstalks off at the rhizome. Snip off any dead roots but leave the plump roots intact.
If you find soft, mushy spots (bacterial soft rot) in your rzs, either discard those rzs in the trash (do NOT compost), or cut the mushy parts out. If you do decide to keep otherwise valuable but rot-infected rzs, soak them in a solution of 1 part household bleach to 9 parts water for 30 mins, then rinse in clear water.
After you have separated, inspected, and cleaned up your rzs, lay all of them out in a shady, dry area for a couple days to allow the cut wounds to scab over before transplanting.
You should transplant these irises into an area providing at least 6 hrs of direct sunlight a day. Prepare a new planting area or rejuvenate an existing bed by making sure the soil is well-drained and properly fertilized. Though iris gardeners often dig a bit of superphosphate into the soil to feed the rhizomes and help promote future bloom, it's actually a wiser tactic to fertilize according to the needs of your particular soil. This can be determined through a soil test performed by your county extension agent. Avoid high nitrogen fertilizers. Excessive nitrogen can promote bacterial soft rot in bearded irises.
When you plant your irises, make sure the top surface of the rhizome is level with or just slightly below the soil surface. If you bury the rhizome too deeply, the plant may refuse to flower. Do NOT mulch directly over the rhizomes. Mulch will tend to retain too much soil moisture right around the rhizomes and promote bacterial soft rot (unless you live in a hot desert climate). If you have the room, plant your rzs about 2' apart with no other plants nearby to overgrow them and compete for soil nutrients. You can also plant 3 separate rhizomes in a triangle 1' apart with the leaf fans facing outwards to produce an instant clump effect. Water the irises deeply once a week for the first month if there is not adequate rainfall. Avoid frequent, shallow waterings. Overwatering is another common cause of soft rot problems.
Just so you understand how the bearded iris life cycle progresses - each individual rhizome will only produce one flower stalk during its lifetime. After (and sometimes before) it flowers, it will turn its energy toward producing "increases" (new rhizomes growing from the sides of the "mother" rhizome). After these new rhizomes grow to blooming size and eventually flower, they will then become "mothers" and grow increases of their own. That is how single rhizomes turn into clumps over the course of a few years and why they need to be divided when the clumps become overcrowded and deplete soil nutrients.