You certainly have your favorite music style and artists, you hear again and again. You learn about new music from the media - radio, tv, magazines, blogs (Thanks, Chris, for your Tip Epica , I never had found them myself) - or from recommendations of your friends.
One alternative to come across new music and artists, which you probably like, is last.fm.
When you enter your favorite artist into the search field, last.fm searches for him and delivers some information and songs:
But here I want to recommend you the "Play similar artists" function:
Further more you can use other users' tags to discover new artists:
If you click e. g. "symphonic metal", you can use the so called "Tag Radio" ot the "Track Playlist" or you browser other similar tags:
Happy "Music surfing"