Getting first aid up to 300 really isn't too difficult at all. As well as making bandages, you can make other items that will cure poisons. These are useful for any class that does not have self-heals (warriors, hunters, etc).

Apprentice: First step for first aid. Apprentice will allow you to get your skill from 0-75. In this initial step, you will be able to create and use Linen and Heavy Linen Bandages. Usually when you're first starting out, Linen drops frequently off of any humanoid creature, so there should be plenty of materials floating around. If you're having problems, you can usually find stacks of linen on the AH for a reasonable price.

Journeyman: This is the next step for First Aid, allowing skills from 75-150. In this bracket, you will be able to create and use, Wool and Heavy Wool Bandages, Anti-Venom, Strong Anti-Venom (learned from a book), and silk bandages at the very end. Wool is a fairly frequent drop as you progress up in levels, and silk normally drops like a madhouse in Scarlet Monastery, which is a great instance for the 35-40 level range players.

Expert: You get this rank by purchasing the book "Expert First Aid - Under Wraps". You will be able to purchase this book from Balai Lok'Wein in Dustwallow Marsh (Horde), and Deneb Walker in Arathi Highlands (Alliance). Deneb is a little harder to get to, as he's in Stormgarde Keep. Just avoid the elites and buy your book. These vendors will also sell the books for Heavy Silk Bandages and Mageweave Bandage, so it's worth picking those books up regardless. You can also purchase the books from the AH at marked up prices, but I would recommend just going out to the places and buying them yourself.

Artisan: Finally, for now, the last step. This requires that you have 225/225 skill and are over level 35. This step requires a quest to obtain. This quest can be obtained from Arathi Highlands (in Hammerfall) from Doctor Gregory Victor (Horde), or Doctor Gustaf VanHowzen on Theramore Isle (Alliance). The quest, Triage, may take once or twice (or more) but once you get the swing of it, it?s pretty easy. If you do fail your first try, just abandon the quest and accept it again. Once you have completed the quest, you will be able to create Heavy Mageweave bandages, Runecloth and ultimately Heavy Runecloth Bandages. If you earn Honored with Argent Dawn, you will be able to pick up the formula for Powerful Anti-Venom.

Master: For getting your skill up to 375 in first aid. You pick this up in Falcon Watch for the Horde and Temple of Telhamat for the Alliance (both or in the Outlands). These vendors will also sell you the books that you need to get your skills up. So you be able to obtain the books for Netherweave and Heavy Netherweave bandages. I have not noticed any significant shortage of runecloth or netherweave, just about any humanoid in Outlands will drop it.

Always remember, a rogue with silk bandages DOES NOT count as a healer (I don?t care what anyone says).