I am an experienced musician, since 1964, studying, playing and performing, but not recording, so I can only give you a very basic answer to this.  It can get complicated.

Here's a few things:

What you're hearing there is digital recording, not live playing, recorded via multi-tracking processes, tracks side by side. 

It is most likely sequenced, that is, let's just say, "entered manually', rather than actually played out. 

I do not know of any specific software packages.

Look at websites such as Guitar Center, Sam Ash, MusiciansFriend, etc, under 'Software'.  You will see all sorts of sw packages, most very expensive, but you can begin to get an idea of what this entails.

You might be able to download something somewhere for free. Hitsquad.com has some freeware.

Do you play an instrument?  If you don't, I'm not sure you can even begin to do this.  You might be able to sequence stuff, but it's still best to be able to play something to really be able to understand how music works.

Digital keyboards, known as workstations or arrangers, have the ability, and are designed to enable song writing.  Check out digital keyboards on the music sites I mentioned above, workstations and arrangers.