There is no single MLS, so basically they have to get data from the various services located in any given market.
They typically paid for that access though I do know they were cut out of the Milwaukee one a while back.
I think they were scraping data at one point (but I could be entirely off-base there) At the end of the day, they are combing through public records, past sales from MLS and in many cases retyped/copied and pasted by the real estate agent.
Is this the MLS? Or is Zillow scraping realtor sites?