Here are some instructions to setup MinGW on different Linux distributions and *BSD.
On Debian all you need to do is type apt-get install mingw32.
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