get bittorrent and download whole albums if you want to avoid getting caught, downloading from a bunch of different hosts on limewire gets you in trouble
if you do use limewire, make sure not to offer any of your files for sharing, because that makes it so people can find you hosting music for download, and that's where you're breaking the copyright. You yourself aren't breaking copyrights by downloading information that is offered to you.
Bearshare also works
A lot of files you can search for on things like dogpile and bing by saying "find files>mp3s" and searching the name of the song, and someone may just have it hosted on a website. That won't work for anything underground though.
I usually go to the library and get CDs to put on my computer, or just get my friends to stick all their music on to harddrives or flash drives.