Or, you could store garlic in an open brown paper bag or a paper fiber egg carton or a cardboard box - allow for air circulation and keep it out of direct sunlight as that will dry it out faster. Net bags work very well as long as there's not so much garlic in them as to impair air circulation. I don't recommend storing garlic in the refrigerator because the humidity can induce fungal and bacterial problems and the low temperature can cause early sprouting. For more details, check out Storing Garlic in our Growing Garlic webpage. For more details please see the Growing Tips page of this website.
Most garlics harvest somewhere in mid season.
The larger they are, the longer it takes them to cure, that is, dry down. Wait for the leaves to begin dying down - the die down from the bottom of the plant first and then proceed to die down towards the top. When the top 6-7 leaves are the only ones still green and they're starting to look a little past their prime, that's the time to pull them. It is the heat that forces garlic to mature and we usually begin our harvest here in early to mid May and it extends into early to mid July. I would imagine your harvest would begin a month or two later than ours.