Download, install and open a DAW software program, such as Ableton Live, Audacity, Reason or Sonar. If you have a Mac, simply open the Garage Band program included with your computer. Even your iPod and iPad have access to music-making programs through the iTunes store.
Play with loops. These programs typically include a set of pre-programmed set of percussion, drum and music loops; you can also download additional loops from a number of websites. Experiment with cutting and splicing these loops --- mixing, matching and overlaying one on top of another, using the settings in your DAW to speed them up or slow them down to meet your specifications. There's no shortcut: You'll have to play with these loops to get a sense of how they will fit into your musical vision.
Learn MIDI. MIDI connections enable computer musicians to recreate the sounds of any number of instruments --- everything from a grand symphony to a quiet piano to a bass guitar --- without actually playing the instruments. You can use MIDI to lay ornate or simple melodies over the loops you have already created, and stack each track on top of each other to make a signature composition.