To download music, you'll first need to sign up for a service like Apple's iTunes, Microsoft's Zune Marketplace, Wal-Mart.com, Napster, Rhapsody or countless others, and install their software (make sure that the service is legitimate). It's a very step-by-step process that you can find via their website.
Most services are paid subscription services—the average song on the Internet costs less than a dollar, but credit cards and gift cards are the primary methods of payment. That fee can vary slightly, and there is different pricing for a complete CD or choosing a subscription service. For example, Apple offers music a la carte or paying per download, while Napster offers a monthly fee that means unlimited downloads. The choice is up to you and will largely depend on what type of digital music player you might have (e.g. an iPod or a Zune). But when it comes to burning a CD, the service choice is less important since they nearly all offer that feature.