Is it possible to somehow plug a microphone into a computer?
Indeed it is although you may want to make sure that you have a good quality sound card in your PC as a low quality one can often result in a low quality recording of good music. If you have an Audio in or Mic port on your computer – that is the one you use. As for recording software Audacity Goldwave FL Studio for PC Adobe Sound Booth – not free For Mac and the best in its class Garage Band.