At home, store them in the refrigerator no more than two days. When it's time to cook, hold the vegetable by the stem and thoroughly rinse it under cold, running water. Cut or snap off the stem so the artichoke can stand upright. If the stem is not too fibrous, it can be trimmed, peeled and cooked along with the globe. Turn the artichoke on its side and cut off the top inch or so of the globe.
Some cooks clip each petal.
While the effect may be pretty, it isn't necessary and it takes time. It is a good idea, however, to rub the top and bottom of the artichoke with a piece of lemon. This keeps the vegetable green. Also, add one tablespoon of lemon juice or vinegar, per quart of water, to the cooking water. To cook, stand the globe in a deep saucepan with three inches of boiling water.