Douglas, were you looking for a schematic of each part, or just the setup with the blocks labeled? There's setups shown out on the web.
As for as the individual pieces:
The motor is a three-phase AC machine. They're called "DC brushless motors" because the windings are arranged so that the "AC" that they run off of is flat-topped instead of sinusoidal -- this makes it easy to make an ESC that runs off of DC, and is still efficient at full power. Each wire from the motor goes to a winding (or a pair of windings, depending on whether the motor is a Y or a delta configuration), they all carry equal current, which is why they're all the same size.
The ESC is a brushless DC motor driver (inverter) that runs off of the battery with commands from the timer. It's basically three switching amplifiers, with a pair of FET switches doing the grunt work (this is why when you look at the circuit board of an ESC you'll usually see six packages all grouped together at some point on the board). Do web searches on "brushless DC drive schematic" and you'll find something representative.
The ESC is designed to connect to the servo channel of a receiver, so it wants to see square, positive going pulses for a command. The industry standard is for a 1 millisecond pulse to mean idle, and a 2ms pulse to mean full throttle; the pulses should occur at a frame rate of 50 to 100Hz.
The battery is just a battery.
To wire them, the two wires from the battery go to the pair of heavy-duty wires on the ESC. The three wires from the motor go to the three heavy wires on the ESC. The timer (or receiver) plugs into the plug on the end of the three light weight wires from the ESC.
I don't know if this answers your question at all, but I hope it helps one way or another.