When peeling garlic, place the flat side of a large chef's knife or Asian cleaver over the garlic and smack it assertively, but not too hard, with the heel of your hand or your fist. The jolt will crack the peel, making it easy to remove. Pound more forcefully, and you will separate the peel and crush the clove at the same time, which will give your a head start on chopping or mincing. you can also lay a garlic clove on the counter and roll it back and forth with your palm. This loosens the skin, making it easier to peel. Or, drop the cloves into a pot of boiling water for 45 seconds. Drain and cool briefly, then pinch the cloves, and the peel will pop right off. This blanching works well when you have pasta water boiling anyway.
For best results when chopping garlic, use a large chef's knife instead of a tiny paring knife. Turn the clove up on its ridge, then cut lengthwise into thin slices. Turn the clove on its flat side and slice lengthwise again to make short sticks. Now, turn the clove and cut crosswise to mince. The garlic may spread across the board as you chop. Use your knife to scrape it back to the pile and continue chopping with a back-and-forth, rocking motion until the garlic is chopped very fine.
To mash garlic to a paste, use a garlic press. Or cover the cloves with parchment and mash with a meat pounder. You can also smash garlic cloves with a heavy object, then sprinkle with a little salt. Mash with the flat side of a heavy knife.