(You already knew that the bits we eat are the flower buds, didn't you? And that if you don't pick them, the buds will develop into huge prickly purple thistle flowers? And, indeed, that artichokes are edible thistles, domesticated in North Africa and loved by the Romans? Of course you did!)
But beware. Just as artichokes are a delicacy for us humans, the leaves are apparently considered delicious by a whole range of bugs. Mine had a bad attack of aphids this year (far too many for my resident ladybirds to control), followed by leaf miners. I pruned off the oldest, biggest and worst-infested leaves, squashed the aphids on the younger, less affected (which took more hours than you can imagine,) baited the ants again (the Argentine ant supercolony here loves to farm aphids on my plants), and studiously ignored the leaf miners.
I don't know how commercial growers get the HUGE buds that you see in stores. Mine never reach anything like that size; they're more like golf balls than tennis balls. But the first bud on a plant - the first one, on the tallest stalk of the plant - is always the biggest. (Once you pick it, the plant will develop smaller buds on all the side shoots.) You have to use your judgement about when to pick any of them, but err on the side of small and delicate. Remember that the true delicacy is the baby artichoke. And, if you pick them as babies, you'll never have to worry about cleaning the hairy inedible choke out of the middle of the bud. (If you ever have to do it, just cheat by cutting the artichoke in half, then use a sharp teaspoon to scrape out the spiky fluff.)
To pick your artichokes, just snap the buds off the stem, one by one, leaving as much stem attached to each of them as you can without also picking the next teensy baby buds further down the stem, and take them inside to cook.
If you're the sort of person who orders whole artichokes in restaurants and carefully tooth-scrapes the edible bit from the base of the outer leaves until you reach the delicious heart, you get the award for patience. I prefer to trim them right down to one delicious bite-size before I cook them.
Starting with baby artichokes (golf-ball-sized) makes the whole process very simple. Start with your just-picked artichokes soaking in clean water, to flush out any insects hiding between the "petals" of the buds. Drain them. You will need a saucepan big enough to hold about 1/4 of the bulk of the buds, after you've trimmed them. (Yes, you lose a lot. It's good for the compost, though.)
Put water about one and a half inches deep into that saucepan, and a big splash of decent vinegar - preferably cider or white wine vinegar. Then pick up one of the artichokes and start snapping off the leaves, working from the base. After a while, you'll find that the leaves change: they'll be more vertical, and mostly yellow, tinged with green at the top. Stop pulling the leaves off at that point. Cut off the top 1/3 of the bud, and pare off the hairy green outside skin of the base and the attached stem, and any damaged bits. (The stem near the bud is just as delicious as the artichoke heart.) The artichoke flesh oxidizes to dark grey very fast. As soon as it looks cute enough, drop it into the water-and-vinegar mix. Then pick up the next one, and the next, and the next. If any of them are bigger than bite-size, you can cut them in half, or even quarters, lengthwise. When you've done them all, bring the water in the pan to a gentle boil, and simmer for ten minutes. Leave the artichokes to cool in the saucepan for a while, then drain them into a pretty dish and pour some fairly decent olive oil over them as a lovely glistening coating. You can add salt and pepper then or later. Then put them in the fridge. They seem to taste better once they're cold, and even better the next day.
You could add them to salads, but you'll probably find that there are fewer in the dish every time you open the fridge, and by the time you come to construct the salad, there's only ever one artichoke left. (I blame the fridge elves.)