I got this far:
Artichoke Fail
But… umm… now what? Which part, exactly, do I eat? Did I cut it wrong? Are artichokes always this fuzzy?
I love artichokes, but never before have ever tried to cook one. They were on sale at Whole Foods this weekend, so I thought, “Yum. I love artichokes. I don’t know how to cook them, but surely it can’t be that hard.”
WRONG. I got as far as the picture above and then… stopped. What happens next?
Mollytics! 
I’m not sure about the fuzz… My dad used to steam them whole. Then you pull the leaves off one by one, dip the bottom end in melted butter (mixed with a little lemon juice?) and pull the fleshy stuff at the bottom off with your teeth.
Two good cookbooks for how to cook anything are “The Joy of Cooking” and “Vegetarian Cooking for Everyone” (the latter obviously only good for vegetarian stuff). Whenever I’m facing something I don’t know how to prepare, or a question like “Is this x ripe?” or “How do I cook beets?” I look it up in one of these and pretty much always find the answer.
Another good way to cook them, is to sprinkle some Italian bread crumbs into the leaves, and then steam them in a little bit of water. Also, this might help:
http://simplyrecipes.com/recipes/how_to_cook_and_eat_an_artichoke/