In order to end up with the tastiest, most tender artichoke hearts, you need to start with fresh, moist artichokes. Like all vegetable, artichokes slowly but surely dry out after they've been harvested. As they lose moisture and age, their leaves pull away from the center, the stem wrinkles, and the tender inner heart gets increasingly fibrous, dry, and tough.
Look for artichokes with tight, compact heads and fresh-cut stems. Note that all cut stems will be brown - artichokes oxidize and turn brown very quickly after being cut - you want to look for artichoke stems that aren't dried out.