Pull off the first couple of layers of leaves of the bottom of the artichoke. Use a sharp knife to cut off the stem- as close as you can to the leaves. Use the knife to cut off the top of the artichoke too- just enough to cut off the spikes and create a flat layer on top.
Place the artichoke - top side down-in a steamer basket inside a pan. Add about 1 inch of water to the pan. Bring the water to a boil on high heat, then reduce the heat to low and simmer on low for 50 minutes to 1 hour (or just until a fork can be easily inserted into the bottom of the artichoke).
Remove the artichoke to a plate to cool slightly before eating. Pull off the leaves and dip in mayo or butter. Scrape the tip of the artichoke leaf with your teeth to eat the "meat" of the artichoke, then discard the leaf. When you get down to the "heart" of the artichoke (lots of purple leaves will be showing), scrape out the purple leaves and stringy stuff, then cut the heart into pieces and eat that too.