They must choose between the top two electoral vote getters, each state gets one vote (California = Wyoming).
Interestingly, the Senate chooses the VP from among the top three EV getters, and each Senator gets one vote.
This was done, I presume, so that if the House deadlocked there would always be a VP-elect to serve as President, since the Senate by definition cannot have a three-way tie if each Senator votes.
By the way, Jimmy and Tommy expected this process would be used frequently, and in fact that's how TJ was elected in 1800.
Actually, they can if the number of states is an integral multiple of three (not currently the case, but has been many times in the past).