The easy way to implement a carbon tax is to tax at major sources, like coal mines and oil wells, and let the producers pass on the cost to everyone else. It's not terribly difficult to assess the amount of coal produced by a mine.

It's also fairly difficult to move a coal mine to another country. Of course, people could import their carbon-intensive goods, but most proposals include tariffs on countries without comparable carbon fees. Tariffs like these are explicitly allowed by trade agreements.