A model two-stroke engine is probably the most simple thing to look at in order to understand the principle of operation. The fuel enters thru the carburator and into the crankshaft ! which is hollow. from there it is sucked into the crankcase by the vacuum created from the piston moving up. When the fuel has reached the crankcase the piston is around the top of it's stroke and is forced downwards again from the expantion of burning fuel. As written earlier the two-stroke engine has no valves, but instead ports in a liner around the piston. This liner has from the intake-ports a room between the cylinder and liner which goes down into the crankcase where the fuel is and as there is positive pressure from the combustion this pressure is relieved thru the exhaust-port and out into the muffler or pipe or whatever. This port is located slightly higher up than the intake-port for the purpose of relieving pressure before both ports are open and fuel can enter. (The ports are opened and closed solely based on the position of the piston, by it's movment.) As this pressure gets less than the pressure the piston creates in the crankcase on it's way down, the fuel-air mixture is forced thru the intake-ports into the cylinder on top of the piston and the cycle starts again with fresh fuel/air mixture being compressed. The fuel is ignited by the plug which in model-engines is a plug electrically heated at start, and is kept glowing from the continous heat from the combustion.
Fine piece of mechanics, eh?
Here is a link which shows the principle mechanics of the two-stroke engine:
http://www.buckeye-illinois.com/2%20...0principle.htm