the same way we power millions of cars now - fossil fuels. Instead of those fossil fuels going directly into cars, they would simply go to central power plants to produce more electricity for the grid.
Cars could also carry portable, thin film solar arrays that could be deployed on sunny days to ease the pressure on the grid and trickle charge cars with enough power to get them home.
As more renewable and efficient power generation comes online to handle our electric needs, we could then start eliminating fossil fuel use.
As far as power allocation at the charging point, I like the proposal presented in the article.
An additional way to reduce charging congestion is for vehicles that do not have a long commute home, to punch in only the amount of charge needed to get them home. Once the charging port has supplied that vehicle with maybe a little over what would be needed to get them home, the supply of electricity could be cut off from that car, allowing other cars to move up more quickly in the charging queue.