Our dermatologists at my clinic volunteer their time at our local prison for tattoo removal. Most of the time, they can be removed to a degree with lasers. It depends on the color and type of ink as to how much can be removed. Essentially, the laser is vaporizing a small area of ink and some skin. Each pulse of the laser feels like being snapped with a rubber band, hard. Some tattoos can be completely eradicated while others just end up faded, due to the type of ink used.
If you have to pay for it, it is charged by the square centimeter, and it is expensive and generally not covered by insurance.