Trixxee, I'll jump in first here re artichokes and I'm sure we all have different methods. What works best for me is -
have a bowl of cold water next to you with a little lemon/lime juice added. (the citrus keep the chokes from browning while you work on them.
remove the first couple rows of leaves off the bottom.
cut the top 3/4- to 1-inch off the top; turn around and cut the stem off flush with the bottom of the choke. Place the choke top side down on a cutting board and cut in half and throw both into the citrus water.
Cut the other end of stem off (so both ends are 'clean'); stand the stem up and carefully cut down the stem to remove the outer (tough) part of the stem. throw in the citrus water.
Now, you need to clean each half. With a very sharp paring knife cut around the fuzzy choke removing all the fuzz. the fuzz is just above the stem and is kind of triangular.
Drop all pieces in boiling water, don't cover, allow to boil for, depending on size, 18 to 25 minutes turning over every so often. When a knife pierces easily, the chokes are done.
You can clean the 'fuzzy choke' out after cooking when it's softer and removes a little easier, but then you're working with a hot artichoke and it's messy as hell. That's it!!
Very wordy, but kind of hard to explain.

I'm assuming you know how to eat them tho, right? if not, that will be chpt. 2