If you have an iris that is too big, stopped flowering, or needs moving, in my opinion September is the best month to do this in the UK. This does not mean they cannot be lifted at any other time of the year. I have lifted irises from 6 weeks after flowering, right through to early spring without harming the plant. Lifting them is easy. Simply ease the iris clump out of the ground using a garden fork. This can be quite hard work with larger clumps of irises, so work around it until the clump is free of the soil. Now the clump can be divided it into smaller sections.
Bearded irises are very satisfying to divide. Take the clump, bang off any excess soil, then with your hands gently twist the plant until the rhizomes snap apart. This is rather like snapping bits off a bar of chocolate. Once all the nice rhizomes with green tops are snapped off, throw away the old, central rhizome that flowered (or should have flowered) this year. Then cut the leaves to about the length of a hand and into a spear shape. This prevents the rhizomes from rocking out of the ground when planted. I use a pair of scissors to do this. Now cut the roots to again to about 15cm (6in) long to make them easier to plant, and to stop crows dragging them out of the soil (they think that they are worms).
To replant a bearded iris, simply dig a hole, place the plant in it leaving the top of the rhizome at soil level. Rhizomes of bearded irises need to get the sun in order to form flowers for the following year. Next year's flowers will already be forming, but you are planting for the future. Then replace the soil (leaving the rhizome just exposed). There is no real need to water bearded irises once planted.
I find the best way to divide beardless irises, such as sibirian irises, is to slice them into divisions using a large kitchen knife or, if it is a very large clump, a saw. Small clumps are less likely to survive, so make sure they are quite generous, about the size of a mug is about as right. Cut back the leaves and roots to about the length of a hand and make sure the clumps do not dry out before replanting them.
Dig a hole and place the plant in it just covering the very small rhizomes that are at the bottom of the leaves. This is easy, because this is where the leaves go pale - just like the bottom of a leek. Replace the soil and water in to prevent the plant from drying out.
Lifting and dividing irises is a very satisfying occupation and irises are tougher than they look. I should know, over the years we have moved thousands of irises.