Download the song from the internet, either through iTunes or another means of retrieving an mp3 track.
Import the selected song into the audio editing software, Garageband is easiest to access if you have a Mac.
Create a duplicate track that you will be able to cut and reaarange if you want to layer tracks. Press "Command-D" to duplicate the track.
Cut and split the second track on the timeline, deleting portions of the second layered track that you do not want in your remix. Move around sections of the song on the second track to manipulate the new track.
Press the Spacebar to hear the edits that have been made to the song. Spacebar will play and stop your music, enabling you to fix any mistakes.
Create drum or keyboard loops through the toolbar on the right. Drag the selected loop into a new track on your timeline underneath your secondary track. Drag as many loops into your remix as you want, until you are satisfied.
Lower and raise each track's volume until you are satisfied with how your remix sounds.
Select 'Export' from Garageband's menu, and export the song to iTunes. The track will be mixed and mastered down to one track, and placed into your iTunes music library.