Most airlines select the passengers to be bumped on the basis of "last to the gate, first to be bumped".  Even if you get to the airport early and have a seat assignment, arriving late at the gate makes you a prime candidate for bumping.

If it's vital that you be on a flight, be at the gate before boarding starts, usually 20 minutes prior to departure time.  This is particularly important at peak times (7-9 a.m. and 5-7 p.m.).  For international flights, most airlines require that you arrive at the airport at least 2 hours prior to departure to check your baggage and complete the pre-boarding process. It is wise to be at the gate waiting during this time as well, as many specific announcements pertaining to your flight are broadcast only at the gate, and may be missed otherwise.

If you are still bumped, the airline will attempt to find another flight for you.  If you're put on a flight that arrives within one hour of your original flight time, you will not receive any bumping compensation.  (The airlines allow a one-hour "grace period)

If the airline places you on a flight that arrives more than one hour- but less than two hours – from your original arrival time, you will receive compensation equal to the amount of the fare of your overbooked flight, up to $200.

If the airline can't get you on another flight scheduled to arrive within two hours of the original flight (four hours on international departures), you will receive compensation equal to twice the fare of your overbooked flight, up to $400.

The airline must give you the compensation (cash, free ticket, or voucher) immediately.  By accepting the compensation, the case is probably closed.  It's too difficult to go back to the airline for additional damages. 

If the compensation won't cover the cost of damages you suffer as a result of the bumping, turn it down!

By not accepting what is offered, you will be able to negotiate with the airlines' complaint department, or even sue.  Don't expect a lawsuit to be successful, however, if your only complaint is inconvenience or lost time.  Unless you have exceptional circumstances, it's usually best to accept what the airlines offer at the time.

Exceptions:

The above rules apply only if the flight is deliberately oversold (and even then there are some exceptions).  Airlines need not compensate you if:

1. You have not complied with ticketing, check-in or reconfirmation requirements.

2. The flight is cancelled

3. A smaller aircraft was substituted for safety or operational reasons.

4. You are put into any section of the aircraft at no charge.

5. The flight involves aircraft with 60 seats or less.

6. The flight is to the U.S. from a foreign country.