Grooveshark has deals with a few of the major record labels. They get paid everytime grooveshark plays a song. They have been sued a couple times in the past and now have deals with most of these labels.

Grooveshark makes money through their VIP, advertising, and promotions put on by the artists themselves.

Technically they are not sharing music since you cannot download it, which is why I would guess they get around a lot of things that way.