The C language spec alone is not sufficient to build a useful system. You're also going to need some kind of operating system interface (defined in POSIX), binary format (ELF), and so on.

The specification that you're both trying to find is called the "System V Application Binary Interface, AMD64 Architecture Processor Supplement" and is found here: http://www.x86-64.org/documentation/abi.pdf

There are similar variations for other architectures. Microsoft does something different, I don't know where their spec lives.