How exactly does the pull-back motor (12787) work?
Another type of pullback motor has a detailed structural disassembly here: Imgur album.

I think your motor should work mostly the same way, but I wasn't able to source such internal pictures.



LEGO Micro Pull-back Motor Reassembly



Micro Pull-back Motor Parts

Gear A: Pin shaped like 'E' for attachment to Spring on Chassis
Gear B: Smallest (of 2) gear with a pin
Gear C: Largest gear with 2 levels, smaller gear at the bottom, larger gear on top, with teeth for meshing with Axle F
Gear D: Smallest (of 2) gear with a hole
Gear E: Medium gear with 2 levels
Axle Assembly F
Gear Assembly G

Not shown: 5 X-head screws
Note: Gear A may be detached from Spring. 
I attached it such that it won't fall out when flipped upside down.



Install Gear B
Place Gear B with pin downwards into slot in Gear Assembly G



Install Gear C.
Place Gear C into the hole in Gear Assembly G.
The larger gear is on top.
Gear C will cover Gear B and mesh with it 
(though Gear B has some play since it is in a slot)



Install Gear E.
Place Gear E into the small depression in Gear Assembly G.
The larger gear is at the bottom, and will slide under Gear C.
There is a pin facing up. Gear E will mesh with Gear B.



Attach Gear D to the Axle Assembly F.
Gear D has a small hole which fits on the pin on Axle Assembly F.



Attach the Axle Assembly F to the Gear Assembly Cover G.
Flip the Axle over. 
Gear D should stay attached to the Axle Assembly.
Align the Axle Assembly and snap down on the protruding pin on the Gear Assembly.
Pinch the two parts (F &amp; G) together at the lower section using thumb and index finger, and try to spin the axle. 
The gears should only rotate when the axle is spun in one direction, and not the other.



Reattach the Gear Assembly G to the Chassis.
This step is tricky. 
You will need to pinch the Gear Assembly to keep parts in place,
then place the Chassis on top of the Gear Assembly G, and move it around
until Gear A connects with the correct hole and mesh with the other gears.
Then, holding everything tightly, flip it over, and start installing and tightening the screws in a diagonal pattern.
Don't over tighten the screws, you should install at least 3 screws first (one on top, two at the bottom), and test that the spring is engaged with Gear A and you get a pull back action when the wheels are turned.
After that, install the rest of the screws and tighten all of them.



The pull back action works, but I can't figure out how to fix the torque on the spring. 
So the car is no longer a race car but a jalopy!