They've had their say, now I am left with empty stalks. Do I just trim off the blooms? It has been suggested that once they bloom, I cut all of them off at soil level. What do I do?
You can cut the bloom stalks (only the bloom stalks!) down now. For tulips - do not cut the foliage; the leaves are needed to feed the bulbs so they can restore themselves and return next year. Once they yellow and shrivel, then you can either cut them down and clean up the area or plant other things around them to hide them.
For the iris, cut the bloom stalk only and any really dry and dead looking leaf, The fans of leaves should stay upright and green and continue to grow throughout the season. I only cut my iris down when I do the fall cleanup.