If you know you'll be cooking throughout the week, peeling garlic cloves is a terrific method to prepare beforehand. Peel the papery, thin skin off the clove after breaking it apart. The peeled cloves should be placed in an airtight container or plastic bag, sealed tightly, and kept in the refrigerator. Within 5-7 days, use.
Peeled garlic cloves can be placed in oil and kept for up to 4 days in the fridge or several months in the freezer. Label chilled garlic-in-oil concoctions with the date of preparation (or, preferable, a "discard after date" label). Garlic shouldn't be kept in oil at room temperature.
When stored properly, intact bulbs can be kept for up to 8 weeks. Use the cloves as soon as the bulb is opened. Breaking a garlic bulb open to remove cloves will significantly shorten its shelf life. Broken cloves will stay fresh anywhere from three days to a week.