DOS did not include a compiler, that's why it's not mentioned in the documentation (though PS/2 did have the ROM BASIC). You had to acquire one separately. There were many options available back then, and a few still exist these days. Here's a couple which are more or less usable IMO:
DJGPP is a port of GCC to DOS. However, it requires a 80386 so it's not suitable here. It seems there was an attempt to produce a 16-bit port but it was not finished.
OpenWatcom is a C/C++ compiler which can target 16-bit DOS. You can actually run the tools on your PS/2 box, or cross-compile binaries from Windows or Linux.
Old versions of Turbo Pascal and Turbo C++ are available from Embarcadero Software Museum. These were very good compilers for their day and included a nice text-mode IDE with integrated interactive debugger.
Quick Basic was a Basic compiler for DOS from Microsoft. It's available on many abandonware sites but I'm not sure about the legality of using it.
Microsoft Visual C++ 1.52 was the last version of Visual C++ to support 16-bit DOS and Windows programming, and it's apparently still available for MSDN subscribers.