There are many ways to get the tens of thousands of Internet radio stations. The most basic is to navigate to a channel's website and listen there. The easier way is to use a program like iTunes, which has a section devoted to Internet radio, with stations sorted by category and genre. Many TVs and AV receivers have built-in Internet radio connectivity. There are even products from companies like Logitech that are specifically just for Internet radio surfing.
Audio quality varies greatly, though it is often highly compressed, using a lossy codec similar to MP3.
Two of the more popular Internet radio stations are Pandora and Slacker.