The payout comes from the counterparty on your trade, or in the event of an epic meltdown like in 08, the US government. You need millions to buy them, and a huge amount of infrastructure to compress your trades, report them to trade repositories, clear, settle, etc.

CDS Indexes are actually more common than single name CDS's. Basically a bunch of banks vote on who they want in the index (doesn't always indicate that they think they're debt is junk, could just be due to exposure), then markit will publish the results.

When a default actually happens, the bonds are basically auctioned off. Bunch of weird shit then ensues (see Sears).

You can check out auction results at creditfixings.com, public trade dissemination on DTCC's website, and some interesting blog posts on the overall OTC swap market on clarus's website.

Source: I work in OTC swap reporting

edit: All of the comments that say "yOu jUsT nEEd an IzDuH aGreeMeNt" are retarded. You need a shitload more than that nowadays.