Miners rush to verify that it's part of a valid chain and include it in the next block. Once one of them does so it's in their self interest to start building a new block on top of that one.

If one of them starts screwing around and produces a bad block the rest of the network will reject it since they can only possibly lose valuable computing resources by pursuing that fork (with very few exceptions).

Consensus is achieved by large numbers of people acting in their own self interest. There is no requirement to have one guy running it all and just hoping he doesn't decide to screw me.