Coal Power Plants are city improvements in the Power category. They are relatively cheap to build and operate, but create a lot of pollution.
Coal Power Plants cost $5,000 and no resources to build. Each turn they use 0.1 Coal per 100 Infrastructure that they're powering and $100. This adds up to 1.2 Coal per 100 Infrastructure and $1,200 a day.
Coal Power Plants add 8 points to your Pollution Index.
Each Coal Power Plant can only power up to 500 Infrastructure levels. Once a city reaches 500.01 or greater Infrastructure it requires at last 2 Coal Power Plants to stay powered.
To fuel a power plant, you must have the applicable resource available in your nation's inventory. For example, in a city with 1 Coal Power Plant and 500 Infrastructure, you'd need at least 0.5 Coal on hand for your city to have power. Your power plants do not use the Coal you produce every turn; instead they rely on what's available in your nation currently.