A friend asked about testing tap water in her apartment. Since we've done this in our place already, I figured I'd share the information.
You don't need to go and buy a water testing kit; the City provides a free kit and the postage and service is all included. Whenever you are ready to take the plunge, call 311 to request that the Department of Environmental Protection send you a free water test for lead. You can also request a fact sheet about lead in your home.
The instructions are pretty simple, but make sure to follow them closely. Testing water should take place in the AM, before you use any water in the household.
Some other general tips are to let water run for a little bit before drinking it; that way any traces will be lessened. Cook with cool water, not hot water. Hot water dissolves lead faster, so it can sneak into your cooking. There are a bunch of other fun tips at NYC's website for the Department of Environmental Protection.