[qiqitori]

If it's C, cflow (example usage: cflow .c .h) and doxygen (needs some config, but there's a GUI) could come in handy. Doxygen is capable of generating call graphs if you install some external dependencies.

If it's a different language, you could try looking around in the docs if anyone's generated callgraphs, or you could look up ways to do so.

To trace the code you could use a debugger -- e.g. if it's gdb just issue the command 'start' and then step through from the main function to see how things go. Or (assuming it's something like a C program) you could get an strace (example usage: strace -vvvttf -o strace.log ./program) and maybe get a feeling for the config/etc. files read or written to, network services accessed, etc.

It would help if you could tell us what kind of program it is, or what kind of programming language it's written in.