I live in the heart of Artichoke country and we eat them at least once a week in season. I usually steam them in a pot. Make sure you check the water level so it doesn't boil dry! For a medium size choke it takes about 20 to 30 minutes to cook thru. You can check by either pulling on the outer leaves, if it comes loose its done or by poking the bottom into the heart and if the fork goes in easily its done. Don't overcook as the heart will get mushy.
We eat the leaves right off the choke at the table. My hubby and I each get one and we share with DD. We dip the leaves in mayo with either soy or whischister(sp) sause mixed in or a wasabi mayo and bite the soft part off. Have also had them steamed in a olive oil and herb mixture and served with a horseradish sause. All good! When you get to the fuzzy middle, scrape it off and you have the heart to eat. Unfortunately, my DD has discovered this delicacy and we now have to share
Here is a site to help you out: http://www.artichokes.net/facts.html
Good luck! They are Yummy!