In order to vote, you gotta register. It's pretty easy, but this step is actually where many people get hung up. They assume it'll be a laborious process, like going through the DMV or accidentally saying "large" at Starbucks. Luckily for us, it's quite quick. You can do it in a veritable jiffy right over this way:
https://voterreg.dmv.ny.gov/MotorVoter/If that doesn't work for you, you can find more info here:
http://www.elections.ny.gov/votingregister.html