I was wondering about this specifically for building software in Debian (the installed Debian system can be a 32-bit version with a 32 bit kernel, libraries, etc., or it can be a 64-bit version with stuff compiled for the 64-bit rather than 32-bit compatibility mode).
Debian packages themselves need to know what architecture they are for (of course) when they actually create the package with all of its metadata, including platform architecture, so there is a packaging tool that outputs it for other packaging tools and scripts to use, called dpkg-architecture. It includes both what it's configured to build for, as well as the current host. (Normally these are the same though.) Example output on a 64-bit machine:
DEB_BUILD_ARCH=amd64
DEB_BUILD_ARCH_OS=linux
DEB_BUILD_ARCH_CPU=amd64
DEB_BUILD_GNU_CPU=x86_64
DEB_BUILD_GNU_SYSTEM=linux-gnu
DEB_BUILD_GNU_TYPE=x86_64-linux-gnu
DEB_HOST_ARCH=amd64
DEB_HOST_ARCH_OS=linux
DEB_HOST_ARCH_CPU=amd64
DEB_HOST_GNU_CPU=x86_64
DEB_HOST_GNU_SYSTEM=linux-gnu
DEB_HOST_GNU_TYPE=x86_64-linux-gnu
You can print just one of those variables or do a test against their values with command line options to dpkg-architecture.
I have no idea how dpkg-architecture deduces the architecture, but you could look at its documentation or source code (dpkg-architecture and much of the dpkg system in general are Perl).