Compile AdaChess from source is easy, just follow this instruction! AdaChess has been written entirely in Ada, so you need first to obtain an Ada compiler. The most common one is GNAT that is available both from getadanow.com (The GCC compiler, provided as TDM-gcc) and from adacore.com. I suggest you to download the adacore version with the Gnat Programming Studio if you want to manage the source; however both are the same and I use both of them while testing.
Once you got the compiler installed, then open the console of your operating system and type
wherever you are under a GNU/Linux operating system or a Windows one.
Please remember that AdaChess is still compiled in 32 bit because the Integer size specification is still unknown. If you want to compile AdaChess in 64 bit you must obtain the tdm-gcc compiler and compile using the target amd64 instructions (-m64) The full compile command is
gnatmake.exe adachess -gnat2012 -gnatp -gnatn -O3 -funroll-loops -fomit-frame-pointer -m64
where gnatmake is the compiler, adachess is the source file adachess.adb (you can omitt the extension name), and other boring stuffs needed for optimization reasons.