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