Enroll in the airlines' mileage programs. Airlines offer discounted upgrades to loyal customers. The more you fly, the more discounts you may receive.
Book your travel for the morning. Flights in the early morning hours tend not to be overbooked. Often, chances are that additional seats will be empty.
Arrive to your flight one hour prior to departure. Put in a request with the flight attendant or airline gate staff. If the flight is not full, you will be one of the first on the list to move to a higher class.
Be courteous. Airline staff may be more willing to upgrade you for free or a discounted rate if you are nice.