Flavored steaming water adds succulence to these. The dipping sauce is a little different from plain mayonnaise or melted butter (although those are very good, too).
Fresh artichokes should have tightly closed heads and not be withered-looking.
To make a nice presentation, cut an inch off the top of the artichokes with a sharp knife, and snip the thorny tips from the leaves with kitchen shears. Cut the stems off flush with the bottom of the artichokes, then cut off the dark, dried-out ends of the stems. Steam the green sections of the stems right along with the artichokes. Sometimes the stems taste good and sometimes they don't, but you won't know unless you cook them. Try a bite of the stems when they are tender. If they taste good but are fibrous, peel them with a sharp knife. If they are good, you have bonus bites of tasty artichoke. If they taste bitter, just add them to the compost pile.
A teaspoon is the perfect tool to scrape off the fuzzy center after eating the tender parts of the leaves. Please remove the fuzzy choke with care. As my father used to say, "That's the part that choked Arty." Then you can eat the artichoke bottom. That is your reward for all the work you did to pull off, dip and nibble the leaves one at a time.
I have cooked them this way for a long time and am not sure where the idea came from, but it was probably Julia Child. The sauce is from my DBF. His brother made it when they were boys at home. It's good on broccoli, too.