You can buy the Armorsmith at the shop, up to a maximum of 6, but it changes cost as you buy more of them. For Details on these see: Buildings - Armorsmith.
You can select which armor to craft as long as you have gathered the required materials and Gold needed for the crafting process.
You will need to wait for the crafting of your armor to finish. How long this takes depends on the rarity of the armor. The higher the rarity, the more time it needs to craft.
If you don't want to wait for the timer, you can pay Gems to finish the armor instantly. This costs 1 gem for every 30 minutes. (example: If your armor finishes in 31 minutes, you'll have to pay 2 gems to finish it instantly.)
If you have multiple Armorsmiths, you can switch and craft another piece of armor while waiting for the first one.
When the Armor has finished crafting, you can either choose to equip it right away, or save it for later.
You can upgrade your Armorsmith by tapping on your Armorsmith and selecting the option "Upgrade". Upgrades cost Gold and Gems, and are instantaneous. Upgrading will make the Armorsmith craft armor 5 percent faster ( for example, if your armor took 100 minutes to craft, it would now take only 95 minutes to craft) and costs 5'000 Gold. The second upgrade will make the Armorsmith 10 percent faster ( for example, if your armor took 100 minutes to craft, it would now take only 90 minutes to craft) and costs 10 Gems