You'll know when to harvest the garlic when the tops of your garlic plants start to die back and turn brown. When you see the leaves starting to decline, stop watering. I know this is impossible if it rains, but do the best you can. This dry spell will help to cure the garlic.
Harvesting too soon will result in smaller cloves that doesn't store well. If you leave the bulbs in the ground too long then the cloves may be bursting out of their skins, leaving them open to disease.
Always dig your garlic, never try and pull it out or so I learned after I pulled them out? Not sure why you are supposed to dig rather than pull but that's the gardening rule. My soil is pretty sandy so it was fine but perhaps if you have soil that tends to be more clay in nature it would harm the bulbs.
You can remove the outer skin but no more than one layer. The roots can be snipped off with scissors. You will need to bend the stalk while it is still pliable or you'll never be able to braid it. Bend the Garlic stalk to break down the fiber. Braid the garlic stalks just like you would if you were French Braiding your hair.....over and under...over and under. Tie off the braids with a piece of twine. You can hang your garlic once braided.