You have two choices:
1) By them from AH. However, since this is your first character you probably don't have the cash to spare. In order to level quickly you're going to need to make a LOT of armor. But, you're not going to be able to sell it all on AH unless you put really low prices on it. So, you'll probably not make enough money to pay for the mats. Also, you'll end up driving the prices really low which will hurt everyone in the long run.
2) Farm them. The way to find the best sources is right at your fingertips. Type in the mat that you're looking for into the search box. It'll provide a listing of where the mat can be found and the drop rate. One thing you'll need to be careful of is that some of the high drop rates are from single MOBs. You want to look for MOBs for which there are a lot of them. Also, check the notes that people have entered and many times they'll tell you where good farming locations are.
One thing you also want to try to do is combine farming with your quests. If you have a quest which requires you to kill x number of beasts, and those beasts can be skinned for what you want, then kill more of them. You'll get extra XP for the effort and it's not as boring as straight farming.
As far as what to do with the product you make, one thing is to sell them in bulk to mages so they can decompose them into materials they need. You won't make as much on an individual piece, but overall you'll do okay. Plus bag space is going to be at a premium since you can't stack what you make (with the exception of armor kits)