The paid survey process is fairly straightforward. You sign up with a paid survey site, and complete a member profile. Then, they send you an e-mail any time they have a survey that matches your profile. A typical e-mail invitation will include an estimate of how long the survey will take to complete, specify how you'll be compensated for your time (if you qualify), and provide a link to the survey. Expect to spend 15-20 minutes per survey on average.
Payment for surveys can vary widely from site to site and from survey to survey. Expect to be compensated one of three ways: with cash (anywhere from $1 to $50 per survey), with points that can be redeemed for prizes, or with sweepstakes entries. In some instances you may also be rewarded with new products to try.