Confirm that there is a problem, particularly if you hear about it second hand.
Check the STOP switch or button. Be sure it's in the normal "run" position.
Check all keyed or restricted switches to be sure they're in their normal "run" positions.
Check for doorway obstructions. This can include foreign matter in door sill grooves or objects blocking complete closure of the doors.
Be sure you're receiving full power from your utility. Have a qualified person check to see if there is a tripped breaker on the main power supply.
Contact people in the car. Make sure no one has accidentally activated the emergency STOP switch. If not, assure them that help is being called.
Call your elevator service company and advise them that you have an entrapment.
Continue communicating with people in the car. Assure them that they are in no danger, and remind them that they should remain in the car until help arrives. Advise them of the technician's estimated arrival time.
DO NOT attempt to open elevator doors or any car-top doors. Wait for help to arrive. You can put yourself or passengers in severe peril if you attempt to remove passengers yourself.
Elevators should never be used during a fire except for firefighters or other specially trained people. The building stairways should be used as the exit route for people who may be in the building duing a fire emergency.
In many earthquake prone areas of the country, local codes require special earthquake features on elevator systems. These may include seismic switches which detect movement and shut down the elevator.