Attach the red clamp to the Positive terminal of the dead battery (step 2)

Attach the red clamp to the positive and black clamp to the negative terminals on the good battery (step 1 and 3).

Finally attach the black clamp to the engine of the car with the dead battery.
(step 4)

Some explanations for the reasons on some steps:

Cars use the metal frame and engine itself to complete the electric circuit back to the battery. The negative terminal is wired directly to the engine. That is why you can connect the negative terminal to the engine. That bolt where the battery connects is a good place, usually to attach the negative cable. This is why you don't want the cars to touch, you don't want to allow the current to pass from one car to the other that way.. you want it through the cable.

When batteries charge, especially when they are charging quickly, they split some of the water in the battery into Hydrogen and Oxygen. The Hydrogen is explosive, and a stray spark from you connecting or disconnecting a cable can set it off. This is not a very likely hazard, but it is one you don't need to mess with. That is why the last cable is attached to the engine a little ways from the battery, where there is not likely to be any explosive concentration of Hydrogen.

The solution in the battery is Sulfuric Acid. That is why you should wear eye protection if you have it. Today's sealed batteries are not likely to leak, explode or spew it out, but why chance it.

Turning on the lights before disconnecting the cables allows any voltage spikes to have a circuit to expend themselves in, lessening them and helping to protect other electronic components in the car.

Buying Cables

A set of cables that have sturdy, strong clamps, a minimum of 6 gauge wires, and are long enough to reach from the front of a car to the front of a car PARKED BEHIND it, about 12 -18 ft., should be the MINIMUM considerations when purchasing cables.

Thanks John for that addition.