Proof of Stake changes things to the point where mining is no longer really a good descriptor of what is going on behind the scenes.

Proof of Stake starts out with a large amount of coins being generated out of thin air. These are then distributed, and owners add nodes to the network by locking in a portion of their coins as their "stake".

The nodes perform transaction verification, and over time a reward block is built out of the transaction fees involved. This is awarded to a psuedorandomly selected node weighted by stake.