When you want a dish to have quintessential garlic flavor that permeates each bite, mince it. You can mince with a knife, or a garlic press.
Either way, you need to free the individual cloves. To do that, press down on the head with the heel of your palm. Apply firm, even pressure so the cloves don't fly all over the place.
To peel an individual clove, cut of the hard stem end where the clove attached to the bulb. Either stop the cut just short of the skin on the other side and peel the skin around to remove it, or make the cut all the way through and squeeze out the clove. The older the clove, the easier the skin releases.
You can also peel it by setting the side of your knife blade on the clove and pressing down until you feel the skin release, though not hard enough to pulverize it, or the skin will get mixed in with the garlic.
To mince with a knife, smash the peeled clove with the side of the knife. Then just run your knife back and forth across the smashed clove, chopping as you go until it's as fine as you like.
If you don't want individual little pieces of garlic and have a press, just put the whole peeled clove (or cloves, if you can fit them) in the press and squeeze. Use your knife to trim away any clinging garlic.
You can leave basil leaves whole and add them to salads and hot dishes toward the end of cooking, tear them into pieces for more capricious basil flavor, or thinly slice them. To avoid bruising the basil, slide a sharp knife down and across the basil with a deliberate, smooth stroke. A clean cut will darken the leaves less than a pounding cut.
To slice basil, first stack the leaves together.
You can either roll them up like a cigar and slice through them to make a chiffonade, or just slice away at them as they are.
