Purchase economy-class seats on your flight. The price for economy class and first class on any given flight can differ by thousands of dollars.
Check in for your flight online. Each airline allows passengers to check in online up to 24 hours prior to departure. Oftentimes, when you check in online your airline will offer inexpensive upgrades to fill empty seats in first class.
Choose to upgrade your seat during online check-in. The price for this is typically $100, though that varies slightly by airline. If there are first-class seats available when you check in at the airport kiosk, the same inexpensive upgrade will also be available for purchase at that time.