What you should probably start with is a MIDI notation application - allowing you to simply input the notes into the PC, which will then play them. I started with a trial copy of one (there'll be links around the site) in about 2002, and I've basically taught myself from there, with no music lessons for ages and only recently taking up piano lessons again.
I compose in a few ways - sometimes I'll think of a melody and rush onto my PC to mess around until I can successfully reproduce it. Other times, I'll record direct from my keyboard to PC via MIDI. Sometimes, I'll even play around with the notation software, and occasionally I'll strike gold. It also helps to have a piano or keyboard ready, and just to mess around until you get something that sounds nice. Have some software on hand first, though - no matter how lame something might sound at first, make sure it's recorded, because you may be able to take it anywhere.
What software allows you to do is just input some notes, as said above, and it will play them back to you - in any instrument, as long as the software has appropriate samples. So, if you get a melody on the piano, but think it'd sound better played on strings, you can just change the sample and you'll have that same melody on strings.
Really, just play around until you find a system that works. Once you're happy that you'll be able to compose, then you can get to it. How you build up a piece is up to you - I tend to start with either a nice melody, a cluster of notes, such as pulsing strings, or a catchy percussion riff. As soon as something comes to me, I'm quick to get it saved onto my hard-drive, as my memory is terrible. You may want to listen to some other works, perhaps ones floating around this site or your favourite movie/videogame music, to see how others manage.