In relative terms, charging an electric car from home is cheap. It is even negligible enough to where the companies that sell you electric cars will do so by comparing the purchase price of an electric car to the cost of a normal gasoline car plus the gasoline over the next several years.
The charging stations on the street usually belong to a consortium with a membership card that unlocks the charging port or it may also belong to your local energy company. Subsidies may also apply to the energy supplied by them.
I pay $0.21/kWh for electricity (electricity generation and distribution charges combined) and usually get between 3.0 and 3.6 miles/kWh (lower in winter; hope to be somewhat higher in summer).
So, electricity is costing me 6-7 cents per mile before considering the inefficiencies of the charger, so likely 7-9 cents/mile at the meter.
For a typical 12K miles/year driver, those costs are order of magnitude the same as the battery pack depletion (for my LEAF anyway).
The charging stations on the street usually belong to a consortium with a membership card that unlocks the charging port or it may also belong to your local energy company. Subsidies may also apply to the energy supplied by them.