You compile things with a compiler ... seriously.
.h are c header files, .c are c code files.
There is generally a little more to it than just trying to compile though ... what are you trying to compile, what environment (linux, windows, mac), do you necessary libraries, etc.
My guess is that if you need to ask how to compile, you need to learn how to program first.
For a free C compiler, try GCC - avaialble for across all common platforms. For an IDE, try the Eclipse IDE (Integrated Developer Environment - basically a gui wrapper around a commandline compiler like GCC).
If you are looking to compile Xbox XBE files, that is a different story again. You'll either need to be a registered Xbox developer with Microsoft, with a copy of the XDK (Xbox Developer Kit), or you'll need to have aquired a copy of the XDK (illegal without having the developer licence), or you'll need to investigate the OpenXDK project over at SourceForge.