Preheat your oven to 425°F (220°C), then carefully wash your artichoke in warm water and pat dry with a towel.
Chop your garlic cloves, chop up or juice/zest your lemon, and measure your olive oil. This is the easy part; it is now over.
Cut the stem off of your artichoke, and then about 1" (2cm) off of the top to open up the leaves. (see attached image)
Now pull off a piece of aluminum foil and place it on the baking sheet, then place your artichoke on top of the foil. The lemon, olive oil, garlic, and salt & pepper are the base flavors from which you'll build your own adventure: tuck the garlic into every crevice you find, and then do the same with the pieces of lemon or pour the lemon juice/zest & olive oil aaaaaall over that sucker. Feel free to salt & pepper to taste now, but you can also do it after baking.
Now pull the foil over the top of the artichoke and sort of wrap it like a baseball, then put the baseball on the tray into your preheated oven and bake for 1 hour. Bake for an additional 15 minutes if your artichoke is massive.
Okay. So here's the hard part. This is how to eat an artichoke: peel off the aluminum foil very carefully, and drain the lemon-olive oil liquid into a little dipping cup. Part of the leaves of an artichoke can be edible (in addition to the more common artichoke heart), so after baking, peel off each of the individual leaves and make a massive pile for dipping into the sauce. Once you reach the thin leaves with no real heft to them, just pull those off and put them in the compost; they're inedible.
Now you should have a large pile of artichoke leaves and a surprisingly small artichoke heart in front of you. Grab one of the leaves and dip the meatier side into your lemon-olive oil sauce, adding more salt and pepper if needed.
Either scoop the artichoke heart onto a plate for later consumption or start dipping your meaty leaves into your garlicky sauce, pulling off the edible part with your teeth. Discard the leaf once you eat off the meat— I know they're beautiful, but I do NOT recommend trying to eat them. But however you bake your artichoke, enjoy the experience!