with regards to remixing, for a commercial track you can generally find the acapella and sometimes the midi file [ googles ] online and if you've got an ear for it you can probably pick out the main chords / melodies on your keyboard - just trial + error. combine that with ableton chops from the original [ practice using eq and filter to isolate parts ] and you should end up with plenty of content to have a crack at it. for more electronic or 'underground' [for want of a better term] stuff just spend a while breaking up the original into samples and go from there. emerging producers can also be very receptive to a quick facebook / myspace message, but it really helps if you have some of your own tunes available for them to check out so they can see what slant you are likely to put on their tune. also you can use the blog network to establish relationships with producers of similar taste and trade track stems etc.
the only other tip i would give, seeing as you mentioned you are just starting out, is to replicate. when you start a new project, have an idea of the type of tune you want to make, find an awesome track like it, load it as a reference track in ableton and experiment with trying to emulate the arrangement, sound design etc. its the very best way to learn quickly how to put a track together in my experience and will push you to try new techniques.
the other only tip - hit the theory thread, there's a huge amount of gold in there, even if you just try and implement a couple of nuggets each time round.