The presence of the
.am files indicates the project is intended to be used with AutoMake. They are the source files for AutoMake, and the only ‘configuration’ files needed if you're building a project.
GNUMakefile.am to see how AutoMake is configured. Generally speaking, you don't need to do that in many cases. The standard
./configure; make; make install and its variants works well.
The GNU Build Toolchain, aka
autotools, (check out the flowchart) is very complex (and its use of M4 is not for the faint of heart — and to think I once used that to make a website). Your best allies are the documentation. All the tools have manpages, but most of their documentation comes in
info pages (say
info automake, or use your favourite info browser).
Have a look at a tutorial for autotools or go browse the official automake documentation.