PART I: LOCATION, LOCATION, LOCATION
Hailing a cab starts long before you even see a cab. It starts the moment you decide you want to hail a cab, because the first decision you need to make is where you're going to hail it from.
Obviously you want the taxi going in your direction, but do you want it coming from the end of your block or the start? If you're on 23rd street between Second and First Avenue, do you want to be on 23rd and 2nd or 23rd and 1st? (The original draft of Moneyball was actually about figuring this out, but Brad Pitt wanted to wear a baseball cap in the movie.)
Always go to the far corner. This may seem counterintuitive—that's a lot of curb for someone else to jump in and beat you to the punch. But while everyone is bunched up on the near corner like it's the last lifeboat on the Titanic, someone is going to get dropped off between you and them and you'll suddenly have first dibs to a fresh, virgin, taxicab. (Actually, the taxi will not actually be fresh. And, it will definitely not be virgin.)