How to play MP3 files in C?

Using FMOD (cross platform), this should be as simple as this:

#include <conio.h>
#include "inc/fmod.h"

FSOUND_SAMPLE* handle;

int main ()
{
   // init FMOD sound system
   FSOUND_Init (44100, 32, 0);

   // load and play mp3
   handle=FSOUND_Sample_Load (0,"my.mp3",0, 0, 0);
   FSOUND_PlaySound (0,handle);

   // wait until the users hits a key to end the app
   while (!_kbhit())
   {
   }

   // clean up
   FSOUND_Sample_Free (handle);
   FSOUND_Close();
}

As a side note, I'd suggest you using C++ over C.

The BASS DLL is really easy to use and will probably do what you need. It is only free for non-commercial use though.

If you need more control, you will need a codec (I prefer libMad) and some sound output API like DirectSound on Windows or ALSA or Linux (or whatever Linux guys use for sound this week)

I don't know if it is "the easiest way", but you could have a look at SDL (along with SDL_sound).

If you are on Windows or OSX, I recommend BASS (http://www.un4seen.com/bass.html)

You can download the library and look at code sample to get started. The "contest" example in C directory is a good start point.