There are at least a couple of options:

Train: http://www.panynj.gov/airtrain/
• Take AirTrain to Jamaica Station.
• At Jamaica Station, take the E subway to the Lexington Ave/53 Street stop.
• Transfer to the 6 subway (through the 51 Street Station) and take it to Grand Central Terminal.
• At Grand Central, take a Metro-North train to Stamford.
The hotel is walking distance from the train station.

Shared Limo: http://www.ctlimo.com/
The Ground Transportation desk is located on the Baggage Level. You can make a reservation by phone there and they will tell you where to wait for your driver. The bus should drop you at the door of the hotel.