Basic Design
Unlike full-sized cars, R/C vehicles are very light for their size. If a 1/12 scale R/C car weighs 10 pounds (which is only the heavy side for a Nitro R/C), its full-sized equivalent would have to scale in at no more than 120 pounds to keep the same size/weight ratio; less than 1/10th of what any full-sized car weighs. Because they are extremely light for their size, R/C cars generally can afford to use two-stroke engines that are lighter, simpler and produce far more top-end horsepower than equivalent four strokes.
Piston Down-Stroke
When the fuel ignites inside of a two-stroke's combustion chamber, the force of the explosion pushes the piston down to create power. When the piston gets to the bottom of the cylinder, it uncovers a hole in the cylinder wall (port), which vents used gases into the exhaust pipe. On the other side of the cylinder, the piston simultaneously uncovers another port through which fresh air and fuel enters.
Piston Up-Stroke
When the piston begins its re-ascension in the cylinder, it covers up both of the ports and compresses the mixture against the combustion chamber roof. This is where R/C engines differ from normal two strokes, and become a sort of gas/diesel hybrid. R/C engines are small enough so as not to need a spark plug; instead, they have a red-hot glow plug that heats the mixture. As the piston compresses the mixture near the glow plug, the mixture reaches its auto-ignition temperature and explodes. This diesel-like operation still allows high-RPM in R/C engines, which are so small in displacement that this "compression ignition's" slow burning of the fuel mixture has a negligible impact on RPM potential.
Fuel
Nitro R/C engines use a mix of either gasoline or methanol (race gas) and nitromethane. Nitromethane is a sort of liquid rocket fuel that contains its own oxygen molecule, allowing the engine to burn far more fuel far quicker than it otherwise would. Nitro is part of the reason that these tiny two strokes can afford to use compression ignition.
Induction and Exhaust
Most R/C engines inhale their fuel mixture through a hollow crankshaft, which has holes drilled in it to allow the mixture to enter the engine's crankcase and thus the cylinder. Many two-stroke Nitro R/C engines also use an "expansion chamber" exhaust, which acts something like a supercharger. The expansion chamber acts like a vacuum to pull air and fuel through the cylinder's intake port, through the cylinder and into the exhaust pipe. The sudden pressure change caused by the expansion chamber causes the air and fuel in the exhaust pipe to do an about-face and cram itself back into the combustion chamber.