Open your garage door using the opener control. If the door opens, but is humming, then the problem is likely a burned-out capacitor. This is a component located in the motor. A technician should be called to fix a damaged capacitor, as it will eventually result in full failure of the opener. If the door doesn't open and is also humming, proceed to the next step.
Remove all screws from the motor housing of your garage door opener. This will usually be located on the ceiling of your garage.
Inspect the internal components of the motor. If the door isn't lifting when opened, it is likely the result of the main gear and sprockets.
Check to see if the teeth on the metal gears are damaged.
Check the sprocket to make sure it is tightly secured to the gear.
Check the chain on the gear to make sure it is properly attached. You can reattach a chain to the gear on your own. However, a damaged gear or sprocket should be replaced by a professional.