I really didn\'t think it would be this difficult. Geany clearly has the ability to create projects, add files to the projects, compile the individual files, but then even a
Compiling a multi-file C++ project using Geany's F-keys requires that you first setup a Makefile and the corresponding settings in Geany (as described in previous answers); after such setup is completed the F-keys in Geany's Build drop-down menu become useful for that particular multi-file project.
If however you just want to quickly compile a multi-file C++ project without having to setup a Makefile as well as Geany's settings, use the terminal at the bottom of Geany to type the command-line instruction for compiling a multi-file project:
uberstudent@uberstudent:~$ g++ my_source1.cpp my_source2.cpp -o my_executable
You can then execute your executable with:
uberstudent@uberstudent:~$ ./my_executable
(Note that the above applies to Geany on Linux; I have not tested the above commands on other operating systems.)