Untarring wham.tgz will create a directory wham/, which in turn contains several directories (wham/ wham-2d/ doc/ nr/).
To build the standard 1-D wham code on a machine which has gcc, you should
cd wham make clean make
(which will delete all object files and executables, and build the wham executable). By default, the Makefile uses the gcc compiler, but I also have flags present for the Intel compiler, plus the native compilers for Irix and Tru64. The latter two have not been tested recently, but ought to work, since at various times this code has been used successfully on various flavors of linux, MacOS X, AIX, Irix, and Tru64. If you find that you need to do anything special to make it work on your particular system, I'd appreciate it if you could let me know so I can add to the Makefile.
To build the 2-D version, say
cd wham-2d make clean make
Several other directories are also created (doc/, which you presumably found because you're reading this, and nr/, which contains a couple of files from Numerical Recipes). You don't need to do anything with these directories.