This post steps through doing the setup for a different library but they apply equally here.
Only the DLL should put into the Windows System32 directory: it is the only runtime requirement.
The header file needs to be found in the path you add to INCLUDEPATH
The link libraries need to be found in the path you add to LIBS with -L, and identified with the -l option (libfftw3.a or libfftw3.lib depending on compiler).
We don't know how you have 'installed' the library on Windows so we cannot give you exact paths. This is what the installation looks like on UNIX:
/tmp/fftw
/tmp/fftw/lib
/tmp/fftw/lib/libfftw3.so.3.2.4
/tmp/fftw/lib/libfftw3.a // link time library, may be .lib for MSVC
/tmp/fftw/lib/libfftw3.la
/tmp/fftw/lib/pkgconfig
/tmp/fftw/lib/pkgconfig/fftw3.pc
/tmp/fftw/lib/libfftw3.so // run time dynamic library, the DLL on Windows
/tmp/fftw/lib/libfftw3.so.3
/tmp/fftw/share
/tmp/fftw/share/info
/tmp/fftw/share/info/fftw3.info
/tmp/fftw/share/info/dir
/tmp/fftw/share/man
/tmp/fftw/share/man/man1
/tmp/fftw/share/man/man1/fftw-wisdom.1
/tmp/fftw/share/man/man1/fftw-wisdom-to-conf.1
/tmp/fftw/bin
/tmp/fftw/bin/fftw-wisdom
/tmp/fftw/bin/fftw-wisdom-to-conf
/tmp/fftw/include
/tmp/fftw/include/fftw3.h // compile time include
/tmp/fftw/include/fftw3.f
/tmp/fftw
/tmp/fftw/lib
/tmp/fftw/lib/libfftw3.so.3.2.4
/tmp/fftw/lib/libfftw3.a // link time library, may be .lib for MSVC
/tmp/fftw/lib/libfftw3.la
/tmp/fftw/lib/pkgconfig
/tmp/fftw/lib/pkgconfig/fftw3.pc
/tmp/fftw/lib/libfftw3.so // run time dynamic library, the DLL on Windows
/tmp/fftw/lib/libfftw3.so.3
/tmp/fftw/share
/tmp/fftw/share/info
/tmp/fftw/share/info/fftw3.info
/tmp/fftw/share/info/dir
/tmp/fftw/share/man
/tmp/fftw/share/man/man1
/tmp/fftw/share/man/man1/fftw-wisdom.1
/tmp/fftw/share/man/man1/fftw-wisdom-to-conf.1
/tmp/fftw/bin
/tmp/fftw/bin/fftw-wisdom
/tmp/fftw/bin/fftw-wisdom-to-conf
/tmp/fftw/include
/tmp/fftw/include/fftw3.h // compile time include
/tmp/fftw/include/fftw3.f
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for which you would set
INCLUDEPATH += /tmp/fftw/include
LIBS += -L/tmp/fftw/lib -lfftw3
INCLUDEPATH += /tmp/fftw/include
LIBS += -L/tmp/fftw/lib -lfftw3
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