Fill a medium saucepan with an inch of water and season it with a few pinches of salt. Insert a steamer basket; if the water comes up through the holes of the basket, pour a little out. Cover the pan and bring the water to a boil over high heat, then reduce the heat to low and let the water simmer.
Meanwhile, trim the artichokes. Pull off any damaged or brown leaves and discard. Using a serrated knife, trim the stems, leaving about half an inch, then cut off the pointy top third. (The artichokes should fit, stem-end up, in the steamer basket with the lid on the pan.)
Place the artichokes stem-end up in the steamer basket, cover, and steam for 20 minutes. Check for doneness by pulling off an outer leaf from each and poking the base of the stems with a sharp knife—if the leaves come off easily and the knife slips easily into the base, the artichokes are ready. If they’re not, steam for another 10 to 15 minutes as needed. Serve with the dipping sauce of your choice. For instructions on how to eat an artichoke, see our illustrated guide.