The best way to vote by absentee ballot is actually to do it in person at your County Board of Elections, which you can do any time the office is open during 30 days prior to the election, up until 5:00PM the day before Election Day.

All the County Boards of Election are on the web here, together with their locations and links to their individual websites, and local hours, etc., are easily accessed there as well.

Absentee-in-person voting is really one-stop shopping.  You will apply for an absentee ballot, receive it, and cast your vote, all at the same time, and helpful election officials will be there to answer any questions and correct any mistakes and you can leave feeling some assurance that your vote will actually get counted which, after all, is the whole point.

You can also to vote absentee by mail, although it's a little more complicated.  First, download a New York State absentee ballot application form, fill it out carefully and mail it in to your County Board of Elections so that they receive it at least 7 days before the election.  Assuming you receive your ballot in time, mark it with your votes and mail it back to the County Board ahead of the election.  The postmark is  what counts, so don't wait until the last minute.

Dutchess County voters can apply for an absentee ballot using either the state form or this simpler Dutchess County absentee ballot application.

Here are New York State Absentee Ballot rules and here is the Dutchess site.

Wondering if you're eligible to vote absentee?  The CountryVote discussion of eligibility for absentee ballots is here.