In the United States, Amtrak Trains operate from city to city and cross-country. When traveling by Amtrak, a student can purchase a Student Advantage Discount Card that is good for a year on any train tickets purchased. Each ticket will receive a 15 percent discount with this card, which students can use online or at ticket offices.
When traveling across Europe, Eurail passes transfer from country to country. Students aged 12-25 can purchase Youth Second Class passes that are cheaper than the average adult pass.
If you are traveling by train, book a car with a bed or sleep on the train between cities. This way you do not need to get a hotel or hostel and it will save you money. Pack light when you are on the train because there is often only room for one bag per traveler.