The basic method is to cut off all the prickly ends and boil for 40 mins or so, until you can easily pull away one of the "petals". Then you sit there, pulling all the petals off and sucking the endy bit out. And when you are left with just the middle lumpy bit, you can have a nibble at that.
They do have a delicious flavour.
In my cookery books, there is a method for hacking the whole thing away before you cook it, so that you only cook the bit you are actually going to eat. But I think you need quite big artichokes to do that (look in Jamie Olivers first book, or Marcella Hazan's Cucina if you have them - they both list a few artichoke recipes too).
Last night I actually cut off all the little artichokes from my transplanted offsets after reading another thread about how you mustn't exhaust the wee plants. So now I have them in a vase at home. I have heard some mention of eating these "baby artichokes" in salads - now, how would that work?
Sarah.