When I buy garlic, I normally put it in a bowl on the kitchen counter or in the pantry, and then pop off cloves as need. Sometimes, if the garlic has been around for a while, I find what looks like green sprouts inside / popping out of the cloves. What is the best way to keep my garlic fresh?
I always store mine in the pantry. I use it frequently enough that sprouting is rarely an issue. If you need it to last longer you can freeze garlic, though I have never needed to.
An unbroken bulb of garlic can last 3-5 months in a cool (55-60 F) dark place. Once broken, the remaining cloves last only about 7-10 days.
Frozen, you can store garlic 10-12 months.
This technique works for garlic, as well as fresh ginger root: use a small grater or zester on the garlic and arrange the pulp on a piece of plastic wrap. Roll the garlic in the plastic wrap and twist the ends so it roughly resembles a long tootsie roll and freeze. When you want to use garlic, snap off a piece and add it to your dish.
This would probably also work with minced or sliced garlic.