Having freshly cooked artichokes with dinner is a fun experience, but I think doing it about once a decade is enough. They're kind of a hassle to eat. I remember having them as a child at my friend Brooke's house. My kids were also very intrigued by them. It's worth introducing your kids to something unique and new, just this once.
Here is the classic version of preparation and method of eating, as given by Better Homes and Gardens.
1/4 c. butter or spread
1/4 tsp. dried dill, tarragon OR oregano
1 Tbsp. lemon juice
Wash artichokes and cut off stems. Cut off 1 inch from the top of each artichoke, and snip off the sharp leaf tips (see photo). Roll the cut edges in a little lemon juice. In a large pan, bring salted water to boiling and add artichokes. Return to boiling, then reduce heat and simmer, covered, for 20 to 30 minutes, or until a leaf pulls out easily. Drain artichokes upside down.
Meanwhile, melt butter and stir in dried herb and 1 tablespoon lemon juice. Serve artichokes with butter sauce.
*Note: To eat artichokes, pull off one leaf at a time and dip base of leaf into sauce. Draw the base of the leaf through your teeth, scraping off only the tender fleshly part. Discard the remainder of the leaf. Continue removing leaves until the fuzzy choke appears. Remove the choke and eat the remaining heart with sauce.