Read the best Alchemy guides for Vanilla / Classic WoW on the fansite WowIsClassic. Guides like "Leveling Alchemy 1-300" will help you to quickly level up your Alchemy from lvl 1 to lvl 300. You will also find guides that list the best patterns / recipes for Alchemy, their drop locations and a lot of tips for alchemy in Classic WoW.
Here is the Alchemy leveling 1-300 guide. Best tips for leveling your profession quickly