I won't lie, trimming baby artichokes involves a bit of work. For that reason, you want to start with the best artichokes possible. Baby artichokes should have tight, compact heads and fresh-cut stem ends. Like most vegetables, they should feel heavy for their size. If you can't prepare them right away, store them loosely wrapped in plastic in the fridge for a few days.
One note: You may be tempted to do each step with all the baby artichokes you have on hand before going to the next step. I suggest that, instead, you fully trim each artichoke before starting on the next one. Trust me, it will go faster and you'll have to keep fewer piles on the counter.
Have larger artichokes on hand? See How to Trim Artichokes instead.