I love artichokes! I usually simply boil them, but you can also do them in the micro. Check for doneness by poking the bottom of the thing with a fork, when they are done, the fork will go in very easily.
To prepare for cooking, cut the stem off as close to the bottom of the bloom as possible, and also, be careful handling them as the ends of the bloom, have spines.
To eat, pull off one leaf at a time, and scrape the fat meaty part of the leaf with your teeth. It takes a bit to get the hang of but they are wonderful. I dip mine in a mix of lite mayo with a bit of dill added, but your tastes may vary.
Hope this helps.