You can use Slacker radio to listen to music and I've seen other users use Pandora. I personally didnt like either on my BB, just cause it seemed to wreck havoc on my berry.
The only way I put music on my berry is to put my music on my media card and back into my bb.
For the most part i listen to music in my media player because slacker and others tend to cut out every now and then(You can cache stations with Slacker). All i do is simply download music from Limewire and then right click on it>send to removable disc x>and thats it. Just like others said make sure you click yes to enable mass storage mode.