Amtrak offers a buy-one-get-one-free promotion for trips on the New York trains only in January and February.

Thanks to the train operator's New York Midweek Winter Travel promotion, Amtrak customers can purchase one ticket and receive a second one for free just in January and February.
For travel every Tuesday through Thursday, the program offers BOGO tickets.

Through February 28th, this promotion is only good on certain trains in New York, including those in Manhattan. 

Basics of deals 

Carrier: Amtrak.

Routes: The Empire Service, Ethan Allan, Adirondack, and Maple Leaf trains are all eligible for travel.

Booking instructions: Immediately on Amtrak's sale page.

Dates of travel: January 3–February 28.

Book by: February 27.

Be aware that you must order one day in advance.
With the purchase of one ordinary adult coach fare, you can receive one free companion rail fare.
The promotion does not apply to reservations made with Amtrak Guest Rewards points. 

How to reserve 

Visit the sale page to begin making an online reservation.
Simply book your train as you would any other train — just be sure to pick a route that is part of the promotion — since there is no promo code required for this sale.

I looked for a path on the Empire Service train in order to research this narrative.
I selected a trip from Syracuse to Penn Station in New York City for the next week. 

Make sure to select the Value coach seat when choosing your train because that is the tariff class that is discounted.
Value seat tickets are refundable if you cancel at least 15 days before travel; if you cancel within 14 days of departure, you'll be charged a 25% cancellation fee.
You can also change your trip plans for free. 

Enhance your purchase 

Use a credit card that rewards you with extra points when you make purchases related to travel, such as the Chase Sapphire Reserve (3 points per dollar spent on travel) or the Chase Sapphire Preferred Card (2 points per dollar on travel). 

In conclusion 

Although this promotion is only valid for trips to or from New York, you can purchase one ticket and receive a second one for free on a number of Amtrak trains this month and the next.