Open up a web browser and navigate to the website for either Amtrak, Travelocity or Eurail. The site you decide to use will depend on a variety of factors, including where you intend to travel to and which site you feel most comfortable booking through. Visit each site in order to get a feel for all three, which will help to inform your decision.
Complete the on-screen forms in order to enter in the information related to the trip you are planning. You will be asked for departure and return dates, locations and number/age of travelers. There may be additional fields for you to customize your search to get the results you are looking for.
Analyze the ticket choices that your search returns. If the choices are outside of your budget, modify your search by changing dates and locations if your travel logistics are flexible. Once you have found a ticket that suits your needs, click the corresponding button to begin booking.
Follow the on-screen instructions to complete the booking process.