I'm pretty sure that a company pays them to administer the survey, and they give about half the money to the survey takers, and keep the rest for themselves.
The company pays for leads, these sites sign up as referrals and get money when they send them leads. They pay you part of that money.
It depends on how the survey but either it will be a simple per lead as already suggested or alternatively if they are a larger organisation and can attract businesses directly then they will charge to design, build, host and run a questionnaire and potentially to also analyse the results for statistical relevance (design can be both the question that appear and what the thing looks like) A lot will depend on what market space they want to operate in as being knowledge of statistical testing is fairly in depth and so the investment required to do this properly in terms of qualified individuals will be significant plus then writing a business rules engine to filter individuals who are completing the forms so your results are representative of the clients desired customer base etc - eg if the clients main market is 18-25 year old males but you are struggling to achieve the desired levels for this market is it better to open it up to 27 year old males or 23 year old females etc)
Companies will pay for your opinion - FACT. When I was at University (10 years ago) I went to a Market Research evening at a friends house and I was paid $40 to give my opinion on this company's marketing material. I also got fed and drunk! The host was paid extra and had all their expenses paid. The internet Paid Surveys schemes are the modern equivalent of this, the host intermediary companies put consumers in touch with the companies who want the consumers view and they take their cut.
Its obviously different for real paid survey places (the places in malls) but I think most of the sites make money from a research company. I don't think its that much money so they make the cash out levels high ($20-$50) and only send you a survey a week. They probably hope that you will lose interest so they don't have to pay you and keep all the profits themselves. This has been my experience
Owners of these survey sites make money by bringing in people (you) to give your opinion on things. Basically, research companies. We (owners) of survey sites are affiliated with these companies, and we get paid when YOU do surveys, because we just brought them business / more opinions. That's as simple as I can put it. If you want to learn more, just contact me on IM.