Pay for an upgrade at the station. Prior to your departure, check with a ticketing agent to see if there are any first-class accommodations available on your train. Amtrak sleeper cars do not have a first-class section; however, you may be able to upgrade to a larger bedroom. Purchase your upgrade and have the station agent re-ticket your trip. European railways are operated by country, and the availability of first-class accommodations varies between rail lines.
Talk to the conductor. If you didn't have a chance to upgrade prior to departure, speak with the train's conductor about whether there are any first-class seats. If space is available, the conductor may be able to upgrade your purchase. If you are in a standard seat on an overnight trip, you may be able to upgrade to an available sleeper car.
Travel on a weekend. In England, the Virgin Trains company offers inexpensive first-class upgrades on weekends and bank holidays. According to the company's website, you may purchase upgrades online or on board the train. Nine other British railway companies offer discounted first-class upgrades on weekends, with a program called Weekends First.