You cut the stems off, cut the tips off (they're sharp!) and peel off some of the outer leaves. Then you put them in a container with a little lemon juice and water and steam them. If you do it in a pan, it takes 20-30 minutes depending on their size. My wife does them in the microwave in about 10 minutes, you can also do them in an instant pot or pressure cooker.
When you can pull off a leaf easily, they're done.
To eat the outer leaves, you peel them off, dip them in a sauce of your choosing (I like sour cream, my wife likes bleu cheese dressing) and scrape off the inner soft part with your teeth. As you get further in, you can nibble on the edge of the leaf a bit, but if it won't easily come off, it is too fibrous to be edible. If you're fortunate enough to find fresh baby artichokes (about the size of a plum), there's a lot more of it that is edible.
When you get to the center, you scrape out the fuzzy 'choke' with a spoon to get to the heart, which is the best part.
Get a big bowl for the scraps you can't eat. I'm told you can compost them, but I've never done it.
Artichoke have an amplification effect on your taste buds, they enhance the taste of everything else you eat.
