The leaves will have a post at the pivot point. That's at the end of the individual leaf. That end will go in the anchor or base plate. The pin that's nearer the middle of each leaf goes into the slot in the aperture ring.
I usually start by putting the housing on a small can just so I can increase the range of motion of my hands. If it's flat on a desk it's difficult for me to get my hands positioned.
You will need a pair of tweezers to handle the blades.
As phfitz mentions the difference in blades. One or two may have a bent tip. These would be the first and last blades. Assuming there are bent tips...........
With the iris facing up the first blade you install must have the bent tip facing away from you. All of the flat blades one after the other and if there's another blade with a bent tip it will be the last blade installed.
After the blades are in place, gently position the blade operating ring on top of the blades. This may drive you to distraction. It requires some degree of patience to do jiggling the housing, sneezing, the occasional earthquake are all common things that require starting from scratch. Speaking of scratching, if you have a cat keep it away 'til you're done.