Play the song you want to sing along in any mp3 player.
Use a recording software like Soundforge (even windows has inbuilt recording software right? ) and hit the record button with the Mike plugged in. Start singing, It will record both. or Wouldn't it??
or you want that software itself adds your voice stream to that of the audio file (which would be less noisy??) If yes, go here I am not sure if this is what you want.