The logistics are pretty easy.

You take the AirTrain (the same train you’d take to get to the car rental facility) to Jamaica Station (about a 10-minute ride; note that there are two trains, one to Jamaica Station and one to Howard Beach, so listen for the announcements to make sure you board the correct train). At Jamaica Station you will need to pay $5 to exit the facility. If you plan to do the same trip in reverse, buy a $10 metrocard from the machine and save the card for your return.

At Jamaica Station, follow the signs to LIRR (Long Island Railroad). After going through the glass doors to the mezzanine level above the tracks, use a ticket machine to purchase an off-peak ticket to Penn Station. (Again you can purchase a round-trip ticket if doing the same trip in reverse on your return). Most times of the day, trains run every 10 to 15 minutes to Penn Station. The trains to Penn Station depart from Track 1.

Once at Penn Station, follow the sign to Amtrak to connect to your train to Providence. On the Amtrak departure level you will find monitors where track numbers are posted, generally about 10 minutes prior to a train’s departure.

There are two types of trains that operate to Providence: the Northeast Regional trains and the more expensive Acela Express. The Acela is a newer and nicer train, makes fewer stops, and gets to Providence about 15-20 minutes faster, but is also more expensive. In either case, be sure to sit on the right side of the train for the best views (and on the left on your return).