At least for horde-side: Once you place your order (which costs 5 Frostweed). Right outside the hut where you placed the order you'll see a little open crate. If you look closely you'll see a little clock/timer above it. Checking your Garrison Report will tell you how much time you have left on it. In the meantime go and quest, let it do its thing. When you come back you'll be able to collect your goodies.
Doing the quest the first time took a couple minutes for it to complete. Second time I did it, the timer told me 4 hours to complete> Not sure if 4 hours becomes the standard, or if it increases each time.
Edit: Done this one a few times, each one takes 4 hours to complete.
Edit 2: Alchemy lab is lvl 2, and work orders do not stack. They are queued. Once one is finished, it will immediately go to the next one. Poop. So just queue up as many as you can and forget about them in the meantime.