Step 1: Rinse and trim
Wash and drain your artichokes, then chop the top layer of prickly spiny bits off. While trimming isn't absolutely necessary, the lack of spines will be appreciated when you peel the artichoke later. It can also help facilitate more even steaming.
Especially with the larger, coarser artichokes, some people prefer to use scissors to trim off the spike from lower leaves as well. I see this as another good argument for buying the smaller, younger, cheaper artichokes which rarely have spikes below the top leaves.