Garrison Resources are a new form of currency used to build and upgrade your garrison. You're gonna want a lot of 'em as you level and play in the WoD expansion, so it's time to get the mining pick out and start farming up a storm. The following methods produce Garrison Resources.
Remember the 10,000 Garrison Resource cap. Obviously anything more than that disappears forever, but it will take awhile to get there.
If you're wondering what you can spend them on, the most obviously is follower missions and building the various buildings in your garrison. Beyond that, you can buy certain supplies (generally for around 100 each) that increase XP while questing. Various merchants in your garrison will sell you materials in exchange for garrison resources.
You can see how many resources you have in various garrison screens, in addition to your character sheet on the currency tab. Resources do not take up inventory space, so don't worry about looking in your inventory for them.
Your garrison produces resources each day, to the tune of one resource every 10 minutes and can hold up to 500. You earn 6 resources an hour and 144 per day.
The Trading Post and Lumber Mill each can generate up to 120 resources each day (modifyable by work order improvements). Smugglers Run (a trading post like outpost) in Spires of Arak can generate random amounts of Garrison Resources, if you're willing to give up the XP boost (thanks John!).
So, if you want to stockpile resources, you can earn either 144, 264, or 384 resources each day by doing very little - however, you will spend over 12,000 resources to get both the Trading Post and Lumber Mill to level 3, which would take you 50 days to earn back - not bad if you play a lot, considering the additional bonuses the buildings provide, but at the same time, it is going to take up two spots and you can only hold 10k at a time.
Follower missions can sometimes reward you with Garrison Resources above what you would obviously spend to send them on the mission.
Completing the story questline in a zone will allow you to purchase a treasure map, which will let you hunt down all the treasures on a map. There is also an addon, called HandyNotes_DraenorTreasures which will tell you where these treasures are without you having to buy the treasure map. This is best done when you first start leveling, as you can't fly in Draenor until 6.1. After 6.1, you can just fly around and get 'em all.
Gorgrond Boulders and Tree Limbs
In Gorgrond, depending on your outpost choice (either Lumber Mill or Sparring Arena), you will find either vines (lumber) or boulders (sparring) that when interacted with will grant resources.
Rare Farming and Bounties
You can obtain resources through killing rares. Obviously, this isn't sustainable, as rares are well rare, but it's an option. Additionally, random quests throughout the world will provide you with garrison resources, but non are repeatable.
Sadly there isn't yet a way to reliably farm materials. You get a massive influx at the start through questing, you can get a chunk through finding treasure, and then after that it's just waiting on 'em to generate. For right now, just be sure to loot your garrison, do the garrison quests, and send them followers on missions!