How does "pushing-start" a dead-battery manual car work? A few days ago the battery of my car went (almost) dead. As it is a manual car, my father once told me that the way to get it going without jumper cables was to push it or let it roll down a hill, sink the clutch, shift to 2nd gear and then let go the clutch.
After the joy of being able to 'revive' the car, I got to wonder of the reason for why this works. All I could think of was Electromagnetic Induction, however I couldn't find anything on the web to support this. I'm sure that there might be all sorts of engineering details, so I'm only looking for the physical principles involved and the basic process that make this work. 
 A: Actually, you can push/roll start a manual car in this fashion with no battery at all.  The momentum of the car is used to turn over the engine when the clutch is released, hence why the car slows noticeably at this point.
Second gear is used to get the engine turning fast enough that the alternator provides sufficient power to run the engine and other electronics, and the pistons move fast enough for the engine to start.
A: 
I'm sure that there might be all sorts of engineering details,

Not really.  An electric starter motor requires a large amount of power to turn the engine over.  If the battery is nearly exhausted, it cannot provide the power to rotate the electric starter motor.
However, as long as there enough power from the battery to run the car's electronic engine controller and ignition system, the engine can be turned over by non-electric means and started.
For older designs without electronic ignition and controllers, no battery is required at all.
I was recently reading about the Coffman starter which used what looked like shotgun shells (cartridges) to start aircraft piston engines.  If you've ever watched the movie "Flight of the Phoenix", there is a dramatic scene involving a Coffman starter.
In early automobiles, the engines were often started with a hand crank.
A: The purpose of the starter motor (using the battery) is to get the engine moving so that the combustion cycle can be initiated.  The combustion cycle is self-sustaining, but it relies on the pistons moving to compress the air/fuel mixture, so you have to get them moving in the first place somehow. By putting the car into gear and rolling it down the hill, the motion of the wheels will transfer to the engine and start the pistons moving, in the same way as the starter motor would.
A: In the days before Electric Rear Window Defrosters, cars still had generators, you could push start the car with a completely dead battery. Generators make electricity, whereas today's cars are equiped with alternators. 
Alternators take electricity to make more electricity. They have a much higher output for today's cars but are useless completely flat. Perhaps if the battery has voltage but not enough to turn over the starter you could push start the car...
My first car had a hand crank and a generator. I do not miss generators, carburators, or points.
