Some suggestions if you are asked to give up your seat or our flight is delayed.
If you choose to do so voluntarily, ask when they can get you booked on another flight, will they provide meals, lodging and compensation.
If your delay is more than an hour and you are not booked on another flight you may be entitled to cash, check, free ticket or vouchers. Information on other delays and compensation here. Demand a check rather than accepting vouchers, and collect it immediately at the airport.
If you are bumped involuntarily, the airline is required to give you a written statement explaining your rights and why you are being bumped. There will be no compensation if the airline then gets you to your destination within an hour of your original landing time (longer if international). American Airlines states you are less likely to be bumped if you check in early.
The Patriot Act makes it a felony for passengers on planes to disobey airline staffers and gives them the right to remove any passenger.
View the airline's contract of carriage terms -
United Contract of Carriage
American Airlines Conditions of Carriage
If you are removed for safety reasons or flight is cancelled for weather reasons there is no compensation.
The airline is supposed to re-book you as quickly as possible.
Above all, stay calm. Getting agitated won't help the situation.