If you have been convicted of a felony and are currently incarcerated, you lose the right to vote. That right is restored when you are released from incarceration. You have the right to vote while on parole (and you never lost that right if you were on probation).
You can check your voter registration status online at the NYS Board of Elections website (https://voterlookup.elections.ny.gov). You can register by obtaining a voter registration form from the Westchester County Board of Elections (below) or from your local library. A current voter registration form is available here in English and Spanish. You do not need any special documentation to register.