how do reciprocating heat engines work?

Answer 1

There are various thermodynamic cycles in internal combustion and "steam" external combustion engines. I suggest you review Otto cycle (four-stroke automobile), Stirling cycle, Clerk cycle (two stroke), Diesel cycle and Rankine cycle (steam), using Google.

Answer 2

Note that the theoretically optimum Carnot cycle is not used in practice. It is simply too hard to implement in a high-rpm mechanical device. As I recall, the Stirling cycle comes closest, but you don't see it used often. The Stirling cycle is an external combustion method.

http://en.wikipedia.org/wiki/Stirling_engine