Whether you are living in New York or just visiting, street smarts will definitely help you feel more at home.
First things first. If you have to go to the bathroom, try a Barnes & Nobles, or a Starbuck's Coffee. Both usually have reasonably clean bathrooms, but your mileage may vary. At Starbuck's you'll need to ask for a key, maybe even buy something.
ride with many people or in the conductor's car (usually the middle car of the train).
Moving the wallet to the front pocket of your pants will reduce your chance of being pick-pocketed.
Pick pockets often use helpers to create a disturbance nearby.
Simply dial 555-1212 on any pay phone and ask for the number of the business or person you are looking for. You don't need to put in any change.