Step 1: Rinse and trim
Wash and drain your artichokes, then chop the top layer of prickly spiny bits off. While trimming isn't absolutely necessary, the lack of spines will be appreciated when you peel the artichoke later. It can also help facilitate more even steaming.
Especially with the larger, coarser artichokes, some people prefer to use scissors to trim off the spike from lower leaves as well. I see this as another good argument for buying the smaller, younger, cheaper artichokes which rarely have spikes below the top leaves.
Step 2: Steam
The cook time will depend largely on artichoke size; you'll just have to guess and check. Check by stabbing through the thickest part of the base with a paring knife- when the knife goes through without resistance, the artichoke is done. These little guys took just under 20 minutes.
Boiling is also acceptable, but leaches more vitamins and minerals from the artichokes and leaves them a bit soggy and harder to handle. If you've got a steamer, use it.
Step 3: Make sauce
Melted butter is traditional, sometimes with lemon and/or garlic.
I prefer something a lighter lemon vinaigrette, which looks/tastes much like lemon/garlic butter:
1 large lemon, juiced
extra virgin olive oil, equal to lemon juice volume
fresh grated garlic (I use lots; do this to your taste)
dab fresh mustard as an emulsifier
dash salt/pepper to taste
Whisk the ingredients together; you'll end up with a gorgeous buttery-looking emulsion. Drop a few tablespoons into individual ramekins to avoid cross-contamination.
Step 4: Remove outer leaves
Peel down the stem as you go; this will come in handy when you reach the heart.
Step 5: Eat large leaves
Remove the leaf, dip it in your sauce, and put it in your mouth upside down so the inside bottom part sits against your lower teeth. Drag your teeth along the leaf, scraping off the fleshy tissue down to the attachment point. Discard the rest of the leaf, as it's too tough to eat.
Step 6: Eat center leaves
Wiggle the cap of center leaves; they should release easily, coming off together. Dip the entire base in the sauce, and eat from the bottom up. The leaves will thicken part way up, making it fairly obvious where to stop eating.
Step 7: Remove choke
Remove and discard the last small leaves covering the choke; they usually pick up some of the fuzzy bits, and so are best simply disposed of. Use a spoon or your finger to scrape out the soft, furry choke without losing any of the tasty heart below.
Step 8: Eat heart
Step 9: Extra bits
Artichokes keep well in the refrigerator, and are great served cold the next day. Just make sure you've got more tasty sauce to serve with them.