This is how we do-it-up in our house:
For any amount of artichokes:
Trim stems of artichokes so that they will stand up straight in a pot. Remove bottom, outer 2-3 layers of leaves (they are tough) and cut off the tops. Then cut thorns off each remaining leaf with scissors. When you are done, they should look like this. (These are Fiesole artichokes):
Rub each 'choke with a cut lemon, then with a cut clove of garlic. Salt liberally. (You can also sprinkle some Herbes de Provence over them.) Drizzle them with olive oil.
Place in pan of water so that water comes 1/3 of the way up the side of the 'choke. To the water add: some whole peppercorns, some lemon slices, and some garlic slices.
Bring to a boil and then reduce to simmer. Cover tightly. Depending on size, they should be cooked in 30-45 minutes. (Smaller ones cook faster.) When a leaf from the center pulls off easily, they're done.
Serve hot with dipping sauce of your choice (we are a lemon-mayo family, melted butter is good, too) and they are also delicious cold.