I'm going to refer you to "Simply Recipes" for a pictorial on how to prepare, cook and eat an artichoke. This is exactly the way I do it except I've never added the garlic or a bay leaf to the steaming liquid; I might try that next time. I also don't bother with all the pretty presentation trimming unless it's for company.
For the aioli:
2 cloves garlic
A couple of pinches of sea salt
1 cup mayonnaise
Juice of 1 lemon
1/2 tsp grated lemon peel
A pinch of cayenne pepper
Using a mortar and pestle (I use my molcajete, you could use a bowl and the back of a spoon) smash the garlic with the salt until it forms a smooth paste. Add all the rest of the ingredients, mix well and chill (I said it was easy : )
Serve the artichoke leaves with the chilled aioli.