So the C API is very simple but that does not mean it is simple enough for me ;)
At risk of saying something obvious that you already know: Part IV of the freely available Programming in Lua 1st Edition is a fairly good gradual introduction to the C API: http://www.lua.org/pil/index.html#P4
It is written for Lua 5.0, but still highly relevant, and annotated in red with most important changes required for Lua 5.1 (and as for Lua 5.2, I believe most of the code will be valid too).
