This first edition was written for Lua 5.0. While still largely relevant for Lua 5.1, there are some differences.
The second edition targets Lua 5.1 and is available at Amazon and as an e-book.
By buying the book, you also help to support the Lua project.

Part IV. The C API Chapter 27. Techniques for Writing C Functions

27 – Techniques for Writing C Functions

Both the official API and the auxiliary library provide several mechanisms to help writing C functions. In this chapter, we cover special mechanisms for array manipulation, for string manipulation, and for storing Lua values in C.