Hi Nathan, 
As I am totally unaware of the extent of you knowledge in the small engines area   so I will start off with the basic parts and locations on a small engine. You will likely know some if not most, but itοΏ½s a good place to start. It may also help others new to the topic in the future.
The crankshaft: converts the up and down motion of the piston and con rod into revolutions. 
The combustion chamber: the chamber that contains the valves, piston, and cylinder wall. It is also the area the fuel / air mixture is compressed in and then ignited in. 
The cylinder wall: the surface that the piston runs up and down on. It is generally made from cast ion or aluminium and in conjunction with the piston rings forms a tight seal between the crank case and combustion chamber. 
The con rod: connects the piston and crankshaft together. 
The crankcase: located in the lower end of the engine it contains the crankshaft and crankshaft bearings, con rod and depending on engine make and model the lubrication system (and cam shaft in 4 stroke engines). 
The cam shaft: is only present in 4 stroke engines. It is connected to the crankshaft via gears (at a 2:1 ratio) and times the opening and closing of the inlet and exhaust valve. 
The lifters or tappets: fill the gap between the end of the valve stem and the cam lobes. 
The valve springs: make sure the valves snap totally shut after the cam shaft releases pressure on the valve stems. 
The collets: the parts that retain the valve springs on the valve stems. 
The valve guides: the circular tubes pressed into the crankcase that house the valve stems. 
The valve stems: the long and skinny circular shaped rod connected to the valves and runs through the guides and into the valve spring chamber. The valve springs and collets are attached to the end of these. The tappets or lifters push  against the end of these and open the valves. 
The sump: the removable cover located on the bottom of the crankcase. It accommodates the bottom crankshaft bearing, and hold oil in the engine. 
The piston. The object that moves up and down in the combustion chamber. It is of cylindrical form and contains piston rings that form a seal against the outside cylinder wall.
The inlet valve: allows fuel / air to enter the combustion chamber at the right moment. They operate on the inlet or induction stroke.  
The exhaust valve: the exhaust valve allows burnt gasses to escape from the crankcase after they are ignited. They operate on the exhaust stroke.  
The ignition coil or magneto: generates high voltage sparks to ignite the air fuel mixture ion the combustion chamber. It is positioned with in a fraction of a millimetre from the fly wheel. 
The fly wheel: the fly wheel is bolted to the other end of the crankshaft to the driven object. The flywheel spins at high revs in front of the magneto to generate electricity. Heavier ones also help to keep the engine balanced. these type of fly wheels are generally cast iron and can be referred to as harmonic balancers. 
The crankcase breather: located somewhere on the crankcase of a 4 stroke engine (generally on the same side as the exhaust, and act as a valve spring compartment cover). They are designed to expel gasses out of the crankcase and are part of the P.C.V system (Positive Crankcase Ventilation) 
 The Carburettor: the unit that mixes and regulates the fuel / air mixture entering the engine. It also contains a throttle butterfly that regulates the speed by opening for faster speeds and closing for slower speeds.
 
The manifold: leads to or from either the carburettor or muffler from the valves. 
The cylinder head: covers the combustion chamber, so a tight seal is formed for compression of the fuel air mixture. When removed it provides access to the piston, valves and cylinder wall. It generally contains the spark plug. 
The gasket: is used to form a air / liquid tight seal around two or more faces. (eg. between the crank case and the oil sump to inhibit oil leaks from the join).  
I hope you have learnt something from the previous writing. I have explained all of the parts mentioned to the best of my knowledge, and most likely have used different terminology to some others. If I have made any mistakes please point them out and I will fix them to avoid confusion. I will explain some more another night, as its getting late now and I cant think of a lot more right now. 
Regards jay