Don't store garlic in the refrigerator.  Put in an a cool, dry, well ventilated spot, in a perforated clay pot or small open wire basket.  It stays fresh for weeks.

To peal, separate into cloves.  Place on a cutting board and using the flat side of a  knife, press down on the cloves.  The skins will split, making them easy to peel.

For large quantities, simmer unpeeled cloves in water or bouillon for a couple of min.  Drain and press gently.  The skins will slip off. 

To remove garlic's pungent smell from your hands or a cutting board, rub with half a lemon.