The first rule in repairing camera lenses is: don't take the iris apart. Well, if you're reading this you've probably broken that rule already. Or you may have needed to repair or clean one of the vanes. Many people think that reassembling an iris is a lot of fiddly, frustrating work, because the vanes are so thin and springy. In fact, it's very easy, but there's a trick.
An iris consists of curved segments called vanes, usually made of springy stainless steel, with a short guide pin on each end. The pins point in opposite directions. They're held between two concentric plastic or aluminum rings. One ring has holes, the other has slots. When the inner ring rotates, one guide pin is fixed and the other slides back and forth in the slot, moving the vanes back and forth.
Trying to fit those vanes back in their holes looks fiendishly difficult at first, but in fact it's quite easy.
Disclaimer: all the iris diaphragms I've seen work this way, but there might be other types out there that are made differently. Many irises in camera lenses have plastic vanes. These are similar, but are best left untouched. The iris shown here was purchased as an optical component. If your iris comes from a disassembled camera lens, reassembling the iris could be the least of your problems.