When do I harvest my garlic?

Quick answer: When half the leaves are brown.

Harvest- Dig up when half of the leaves are brown (including the bottom leaves which have fallen off), usually June 25- July 10 for me. "Turban" garlics such as Tzan and Shantung Purple are usually ready 3 weeks before the rest (June 15 or so). 
When harvesting, remove the biggest chunks of dirt from the garlic by giving a gentle twist to the dirt clump. I leave on the roots and stems. After harvest shade immediately. Hang or put on ventilated shelves for 3 weeks to “cure” with stems on. They must have good air circulation and shade.

How To Store- Clip off the stems after they are cured. Store at room temperature or cooler, out of direct sunlight. Cool basements and garages can work well for storage. The bulbs need air circulation, but storing in paper bags is recommended for long-term storage to keep them from drying out too much. Many people have luck storing in the fridge in paper bags. Hardnecks generally store up to 5 months. Softnecks up to 9 months. Turbans stay firm til December or January, but send up random sprouts starting in November (still great to eat).
Garlic that has been in the ground too long will start to lose the skins and will not store as long but is otherwise fine.
Cleaning-  After curing just rub off the dirt, and maybe one layer of dirty outside skin and they will look gorgeous.