Besides the main Bizhawk.sln, there are a number of other projects, each with its own build method. To develop Bizhawk, you do not need to build these other projects, as they are included prebuild in SVN. You need only build them if you want to modify the cores themselves.
libgambatte: Process libgambatte/Makefile with mingw. Use "make install" to copy to output folder. Alternatively, there is a VC10 solution at libgambatte/libgambatte.sln, but that's not used.
libsnes: During development, run bizwinmake.sh. Edit it as necessary to change profiles and bitness. For making release mode dlls for committing, run bizwinmakedistro.sh. Note that 64bits libsnes doesn't work right now.
quicknes: Process quicknes/mingw/Makefile with mingw. Use "make install" top copy to output folder. Alternatively, there is a VC10 solution at quicknes/libquicknes/libquicknes.sln, but that has audio output glitches.
wonderswan: Load wonderswan/bizswan/bizswan.sln; builds as VC++ (VC10). Output dll automatically copies to appropriate folder. Alternatively, there is a mingw Makefile at wonderswan/mingw/Makefile, but that's not used.
natt: February 2016: the environment I currently use to build all of my mingw stuff, 32 and 64 bit, but not waterbox (which is on linux) and maybe not bsnes (haven't tried in a while) is a vanilla http://msys2.github.io/ install.