The player's Garrison is one of the central features of Warlords of Draenor, coming with its own special Hearthstone, and in many ways taking the place of a faction hub. Depending on what kind of structures you choose to build in your Garrison, you can have your own crafting centers, bank access, auction house, PvP center, and more. However, to build any of them, you need resources.
In fact, to do just about anything with your Garrison you need resources. You need them for buildings, for crafting, and in order to send your followers on missions. So, just how do you get Garrison Resources? Well, I'm glad you asked. There are a variety of ways to earn your Garrison Resources in Warlords of Draenor, some easier than others.
One of the most straightforward ways to get resources is through questing. Some quests give you Garrison Resources as a reward, especially in the early stages of Warlords questing, when you're first establishing your Garrison. In addition, certain bounty quests--some offered by your own Garrison's "Hero's Call" board--will often give resources as a reward as well. As you gain levels and progress through the zones in Warlords of Draenor, fewer quests will offer Garrison Resources as rewards.
While you need resources in order to send your Garrison followers on missions, you also often gain resources from the successful completion of those missions. Resources aren't the most common reward from follower missions--most reward you with gold or extra XP for your followers--but the resources gained from completing missions easily outstrips those spent on sending your followers out in the first place.
Mists of Pandaria introduced a lot of world treasures--hidden, unmarked objects scattered throughout the world that would reward the diligent player with weapons or other items if you found them. Warlords proudly continues this tradition and many of the world's treasures offer Garrison Resources as part of their loot. It would do the would-be treasure hunter good to check out a lot of nooks and crannies in the various zones, as well as the site of your Garrison before you actually begin to build it. There are several caches of Garrison resources available at the Garrisons' sites that you can only loot before you build your Garrison, so leave no stone unturned!
There exist a few rare mobs that can potentially drop Garrison Resources themselves. Far more common, however, are drops that can be combined with crafting materials and turned into a quartermaster to reward resources for your Garrison. What items drop for you depend on what your primary crafting skills are. With each combination you have a chance to produce either an Uncommon- (green) or Rare- (blue) quality item. Rare-quality items earn you more Garrison Resources, of course. The professions represented by drops are: Alchemy, Blacksmithing, Enchanting, Engineering, First Aid, Inscription, Jewelcrafting, Leatherworking, and Tailoring. As you can see, these are all the "production" primary crafting professions plus First Aid.
The Garrison Cache
Lastly, whether you are Horde or Alliance, there is a giant chest located next to your Garrison's main building that will slowly fill up with resources, and you can open it periodically to lay claim to its contents. The longer you leave it, the more resources will be there. Horde-side, this mechanic is explained by saying that your continuously-working peons will place the resources they harvest in the chest, and you can grab them whenever you wish. Alliance-side, there doesn't seem to be any explanation, it's just there. The Garrison Cache is a particularly nice feature, especially if you've forgotten about it for a couple of weeks. In addition, certain Garrison buildings (such as the Mill) will increase the rate at which you gain Garrison Resources.
There are plenty of ways to earn resources for your Garrison in Warlords of Draenor, and I wouldn't be surprised if Blizzard added even more of them in future patches. Perhaps we'll see them as boss drops or rewards for certain achievements. Pay attention to the treasures around Draenor, and don't forget to check your Garrison Cache once in a while.