There are two types of springs on Residential Garage Doors. Most common is the Extension Spring. These springs are the type that are suspended above the tracks of the door that follow the ceiling into the garage. They have pulleys, and are extended when the door is down, and compress as the door opens. They rarely break, but have been know to rocket off the door if the lifting wire breaks. They are very common on the smaller (8 x 8) doors.
On the larger doors, you most likely will see Torsion Springs. These springs (sometimes only one, sometimes i a pair) are mounted on a steel shaft, and will run across the header (above the door on the interior) of the garage opening. These springs turn (rotate) as the door goes up and down. They apply lifting pressure to the lifting cables that attach to the bottom of the door at each jamb (side). These springs are VERY dangerous and even the best handyman should not attempt to even adjust these springs! When your door is down (fully closed) these springs are at their most wound position, and look rather harmless. But, if you were to try anything to these springs, the lift wires, or the bottom shoe (the metal part that connects the lifting wire to the bottom of the door) you can be very seriously injured. I have been in the door business for over 30 years, and have heard some very sad, and tragic stories of homeowner attempts to adjust or fix the door to save money. Yes, some have resulted in death.
So please, if you think your quoted price is too high, just shop around some more. Don't try to do it yourself, it's not worth loosing a finger, limb, eye or your life over it.