Getting Started -- Herbing and Alchemy.
Herbing!
The money making profession are Alchemy , Herbing and Mining and Engineering.
To start off you begin with Herbing. Picking herbs will earn you money just with the herbs you pick, but it will also let you increase your ability to do alchemy. Alchemy is a very profitable profession but leveling up your ability to do alchemy starts off with Herbs.
Alchemy is one of those professions that allows you to control the required materials that are the bottle necks to crafting big price items like Vial of the sands.
(Vial of the sands is a craftable 2 seat flying mount that any player can use)
Herbing , or picking plants, is profitable in itself. If you go to the Herbing trainer in storm wind and learn this profession you can start off making gold.
Head over to the city of Stormwind to the trainers marked on the map below and get the ability to pick.