Have a bowl of lemon water ready, and dip your palms and fingers in the lemon water. (This prevents your fingertips from turning black.)
Start peeling off the outer petals. When you reach the section where the bottom petals are tender as shown, chop off the stem and dip it in the lemon water.
The core of the stem is tender and edible, so trim off the outer ring of fiber and dip the core in the lemon water.
Trim off the hard green parts off the calyx, and dip the remainder in lemon water.
The tips of the petals are hard and fibrous, so cut them off.
Cut off the hard parts of the petals (the red parts) at a 45 degree angle, and dip the artichoke in lemon water.
Cut the artichoke in half. If the center is hard (if it's prickly to the touch), cut it off, too.
Soak the prepared artichokes in lemon water, until they are ready to cook.
Artichokes are fresh when the petals are tightly furled and haven't started to open. The stems are edible if they can be cut through easily with a knife.
Artichokes are very astringent, so dip them in lemon water frequently while cooking. Wipe your fingertips with lemon as you work to prevent them from turning black.
Basically, all of the white or tender parts can be eaten. In Step 6, the centers of the artichokes I had were tender even if they were red, so I didn't cut them out.
It doesn't bother me, but if the scent of the lemon is too strong, you could also soak the artichokes in water with 1 tablespoon of flour, or with plenty of chopped parsley.
Story Behind this Recipe
Until I was shown in person how to prepare artichokes, I never thought to cook them myself. I wondered if there were other people like me, so I posted this recipe.
User "Torebiante" told me that American artichokes are large and tough. I used Italian artichokes (carciofi). I tried this method with various varieties of artichokes (3-10 cm in diameter), and this method seemed to be okay for Italian artichokes.