While the 2013 Nissan Leaf is no longer the only battery-electric car on the market, it's the highest-selling one thus far--and far more affordable than the Tesla Model S that might nip at its heels in sales volume by the end of the year.
But like any electric cars that runs solely on power from the electricity grid, the 2013 Leaf is one of the very greenest cars anyone can buy. So far, the EPA hasn't yet issued its ratings for the latest Nissan Leaf. Last year it was rated slightly higher in energy efficiency (at 99 MPGe) by the EPA than than last year's Chevrolet Volt (at 94 MPGe), though both cars have been updated slightly this year. (MPGe, or "Miles Per Gallon Equivalent," is a measure of energy efficiency meant to convey how far a vehicle can travel electrically on the amount of stored battery energy that represents the energy contained in a single gallon of gasoline.)
With the new 6.6-kilowatt charger that comes standard in all but the base 2013 Nissan Leaf, recharging a fully depleted battery now takes only 4 hours using a 240-Volt Level 2 charging station. It may require some house rewiring, but no more than if you were installing an electric stove or clothes drier. On standard 110-Volt household current, a recharge can take up to 20 hours.
The greenness of a particular Leaf will depend on where it's driven; the electric grids of some states are far dirtier than those of others. A 2013 Nissan Leaf recharged on power from the oldest, dirtiest coal power plants is still cleaner--comparing "wells-to-wheels" carbon emitted through the process of creating the fuel as well as powering the car--than the average 25-mpg vehicle. But if you compare to a Toyota Prius rated at 50 mpg, however, a few areas (North Dakota and West Virginia, for example, have exceptionally dirty power), burning the gasoline in a Prius turns out to be slightly better overall. Luckily, California--which will buy more plug-in cars than the next five states combined--has a relatively clean grid, so the Leaf is about as green as you can get there.
As for costs, a mile run on electricity is usually far cheaper than a mile driven on gasoline. But the difference will vary quite a lot depending on the price per kilowatt-hour of electricity where the car is recharged.