American flag irises grow from fat underground stems called rhizomes. You can get more plants by breaking off rhizomes from a large plant and planting them just below the soil with any attached roots going down into the soil below. This is very easy. Trade colors with your friends and neighbors.
Dutch irises grow from bulbs and you have to wait till the bulbs multiply underground. If you dig up your bulbs every Fall and replant in the Spring, your bulbs will never divide.