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.