I'm not sure just how long it has to dry, but quite awhile (at least a month or two?), and it should be stored in a pretty dry place even after that.
On the other hand, I do know that you actually can eat it right away. When eaten right away like that it's known as "green garlic" and is a little juicier, but it's still basically garlic. The drying process is something the garlic needs for storage, in order to keep all winter--it doesn't need that in order to be ready to eat.
(That's part of why I don't know just how long to dry it, in spite of having worked on a farm that grows it--we usually just saved some back to eat & sell green, and as for the storage garlic, we laid it & the onions in the loft to dry in July when they were ready and then forgot about them till October when the pace of work slowed down, and then went up there and boxed up the garlic for the winter. So, I know *that* works...)
Can it get too dry? I hung mine in a back "mud" room to dry for like 2 weeks. It's fairly warm back there-about 80 degrees. I'm afraid I waited too long to brush off the dirt and cut the tops off, etc. Some of it looks kind of yellow and shriveled up.
A few years ago a local garlic grower made a presentation to our herb club. He told us to air dry them in a cool, dry place for a month. So an 80 degree venue probably would dry some of them up. I know I hung some of mine in the kitchen when I first started and they did dry up. Now I use my cellar where it is cooler and they have lasted much longer.