I love Artichokes.  A note on buying them:  I find that the one's with the leaves standing up are better than one's where the leaves are all curled over in a ball shape. 

Now I simply put them in a pot and boil them covered.  When they start boiling I turn the heat down to medium.  I find it takes about 20 to 30 minutes for 1 or two.  I test it by putting a fork in just below the stem and into the body of the choke.  It should go in easily (but not fall apart).  Also I do not cut off the stem, there is good meat down into the middle of the stem.

 Now I like to dip the leaves in mayonnaise.  And I have found that Hellmann's Light mayo (with the blue top) is low fat and taste just like their Real mayo.  Once getting down to the very thin leaves just pull them off and then scrape off the furry part with a spoon...  then step into heaven by eating the heart of this feast.