How to Fourier Transform?

So how does one break a windows wav file into the component sine waves, together with phase and amplitude? People say one has to use DFT, but wikipedia article on DFT contains just some opaque formula, containing e with a complex superscript. How can it be used to produce C/C++-compilar uint32_t array of sine-wave frequencies? C/C++'s exp() cant even exponentiate e to a complex number.

You can implement a complex exponential in three lines, why do you want to write a DFT yourself if you don't know the basics of complex numbers?