Here are some instructions to setup MinGW on different Linux distributions and *BSD.
On Debian do apt-get install mingw32.
The standard MinGW libraries will probably be incomplete, causing 'undefined symbol' errors. So get the latest mingw-w32api RPM and use alien to either convert it to a .tar.gz file from which to extract just the relevant files, or to convert it to a Debian package that you will install.
This includes Fedora Core, Red Hat Enterprise Linux, Mandrake, most probably SuSE Linux too, etc. But this list isn't exhaustive; the following steps should probably work on any rpm based system.
Download and install the latest rpm's from MinGW RPM packages. Alternatively you can follow the instructions on that page and build your own packages from the source rpm's listed there as well.
The *BSD systems have in their ports collection a port for the MinGW cross-compiling environment. Please see the documentation of your system about how to build and install a port.
Having the cross-compiling environment set up the generation of the Windows executables is easy by using the Wine build system.
If you had already run configure, then delete config.cache and re-run configure. You can then run make crosstest. To sum up:
$ rm config.cache $ ./configure $ make crosstest