Hi,
Have you read the thread about compiling on Win32 using MinGW (named 'CVS Builds (every 2nd day)' on the Dosbox Development Forum) ?
in short : see http://www.mingw.org/msys.shtml :
Install msys 1.09, then the latest MinGW and MSys DTK,
Then install the DirectX devel. libraries under MSys (http://www.libsdl.org/extras/win32/common/, download directx-devel.tar.gz)
Then you will also need libSDL (www.libsdl.org) : download http://www.libsdl.org/release/SDL-1.2.6.tar.gz from there, and extract & compile it under Msys/MinGW
Then get a dosbox source tarball somewhere (version 0.60 or CVS), and extract it. Type ./autogen.sh, then ./configure, edit the config.h file to suit your needs, and then type 'make'.
As the initial dosbox.exe is quite large (+- 9 Mb) you may want to remove the debugging info : strip --strip-all dosbox.exe (execute under Msys)
I know this is a quick overview and not a complete explanation (for a more complete explanation, see the thread I mentioned, it only forgets to mention the DirectX libraries)
J.