Are you trying to cook a fresh artichoke or use canned artichokes?
For fresh artichokes, I use the very simple method of cutting the stem off and popping the whole thing in a pan of simmering water for 35-45 minutes. It is done when you can press a knife in the stem area easily. I then pull off the leaves, dip them in melted butter spiked with a bit of lemon, and scrape the leaves with my teeth. Preso, simple. The fancy cookbooks will tell you to cut off the thorny bits on the leaves, but I think I'm mature enough to just avoid the pokey parts. When you have peeled the leaves down to the fuzzy part (the choke), use the knife to scrape the fuzz away and toss it (if swallowed your throat will be itchy for a long time). Chop up the bottom of the artichoke and toss in the butter before eating.
Canned artichokes can be added to salads or sauces.
Food should be fun--Thomas Keller