Slice off the artichoke stem, leaving about ½-inch, and remove about ½-inch from the top. Use kitchen scissors to snip the outer leaves so that they have straight edges. Wash the artichoke under cold running water, gently opening the leaves ever so slightly if you can. Turn the artichoke upside down to drain.
Place the artichoke in a microwave-safe dish. It needs to be deep enough for the artichoke to sit inside and the lid to completely close. Add about ½-inch of water to the bottom. Cover, and microwave for 10 minutes on high (for a medium or large artichoke). Remove the dish from the microwave and let it sit, covered, for 5 to 6 minutes to finish steaming. Open the lid, and test the artichoke for doneness. It is ready if you can glide a fork into the stem and easily remove the outer leaves. If the artichoke is not cooked to your liking, put it back in the microwave for a few more minutes and let it steam for an equal amount of time until ready.
When eating the artichoke, avoid the fuzzy choke. I prefer to slice the artichoke in half and remove the choke with a spoon before eating. Remove a leaf, and scrape it between your teeth to eat the tender flesh. Discard large leaves after eating, but you usually can eat the small innermost leaves whole. You can also eat the artichoke heart, and the stem if it's not too tough.
Cooking time depends on the size of the artichoke, size and surface area of the baking dish, and strength of microwave. I used a large baking dish for my artichoke, so it took longer to cook than it would in a small dish. If you are using a smaller dish, cooking a small artichoke (versus a large or medium one), or have a strong microwave, adjust the cooking time.
If you don't have a microwave-safe dish with a lid, use a glass bowl covered with an upside down glass pie plate. I used a Corning Ware round dish with lid, for reference.