The New York State AFL-CIO coordinates year-round programs of political education, Get-Out-The-Vote campaigns, and non-partisan registration for union members across the state
The most important way for a union member to become active in politics is by making your voice heard at the ballot box.
If you have a New York State drivers license, you can register to vote online through the Department of Motor Vehicles. 
Otherwise you can register by mail or in person at your county Board of Elections, or at any state agency based voter registration center.
More information on registering to vote can be found at the State Board of Elections, including information on absentee ballots and registration deadlines.