Garlic is usually planted in the late fall. I plant during the first week of November.
Separate a head of garlic (grocery store garlic, or a specific variety purchased from a seed vendor) into individual cloves, leaving on the protective skin. Plant individual cloves ~2-3" deep, at least 6" apart. Make sure the blunt, root end is down. Cover with heavy mulch, then ignore all winter long. In mid June to mid July, when the tops begin to die, dig the garlic. Each clove will have formed a new head of garlic. Don't wash them. Allow to dry for a week or three, then peel off the outer layer to remove the dirt.
Garlic comes as either hard neck or soft neck. The hard neck garlic varieties (woody stem in the center) will form a curly flower shaft, called a scape, a week or more before they are ready to dig. Cut off the scapes and eat or pickle them. Soft neck garlic usually does not form a scape. Save the largest head for planting the following autumn. Garlic can store in a dry place for a year or more.
In digging them, I usually dig around them entirely, then use a tool to lift them out of the ground from below. If you try to pull them like onions, without freeing them from the dirt, they sometimes tear apart.
Bob