Select artichokes which are firm and with the tips round and tight. Peel off lower tough petals, trim away bottom of stem. Using a large serrated knife, cut off the leaf tips about I to an inch down from the top, Just saw it off, exposing the tender leaves inside. This helps the steam get in and cook the center. I like to use shears to trim off all the tips of the outer leaves as well.
Have a pan with a steamer rack and water boiling while you do this preparation and get them into the pan right away because cut edges turn black. If you have to wait, rub cut edges with vinegar or a cut lemon to halt the blackening.
Cook at least 25-35 minutes, tips facing down on the rack. Check with fork in the stem end, for doneness. Depends on freshness and size.
Alternatively, you can boil them in a couple of inches of water with a little olive oil and a clove of garlic in the water. Serve warm with melted butter or chilled with mayonnaise.