You'll need to reach level 300 First Aid first, and visit your respective trainer in Hellfire Peninsula!

Alliance

1. Alliance should head out to the Temple of Telhamat to locate (22, 39).
2. Purchase Master First Aid - Doctor in the House (cost is 5G) and get your achievement! While you are there pick up Manual: Netherweave Bandage (cost is 2G) and Manual: Heavy Netherweave Bandage (cost is 4G). These will be used to level to 375 First Aid.

Horde

1. Horde should head out to the Falcon Watch to locate Aresella (26, 62).
2. Purchase Master First Aid - Doctor in the House (cost is 5G) and get your achievement! While you are there pick up Manual: Netherweave Bandage (cost is 2G) and Manual: Heavy Netherweave Bandage (cost is 4G). These will be used to level to 375 First Aid.

Blue post on patch 3.1 states - "You no longer need to learn cooking from books. The trainers have finally done their reading and are able to teach you the same thing."