After pulling the red emergency release cord on a garage door, ensure the door is closed and then manually operate it to reset the system. Once the door is back in the closed position, re-engage the trolley with the opener carriage by pulling the release cord towards the door and reconnect the trolley to the opener carriage. Regular maintenance checks are crucial to ensure the proper functioning of the garage door system, and if there are any issues, seek professional assistance for safety and effective operation.