Select a drill bit that is small enough in diameter to fit into the garage door lock through the cylinder or keyhole.
Insert the bit into the drill and tighten the drill's chuck to hold the bit firmly in place.
Put on safety goggles and gloves. Insert the drill bit into the cylinder where the key would normally go. Close the door and leave the lock in the unlocked position, if possible.
Set the drill on its lowest drill setting to begin, then pull the trigger and drill into the cylinder, putting your weight behind the drill. Continue to drill straight through the lock until the bit breaks through to the other side.
Back the drill bit out of the lock on the garage door, then allow the bit to cool off. Once cool, select a much larger bit and insert it into the drill.
Drill into the garage door lock again. This will displace and/or break the pins inside the lock, making the lock free and able to be taken out of the garage door. You can now remove the lock entirely and replace it.