I got tattooed recently. By a human. Antoine Goupille also got tattooed recently. By a 3D printer modified to do tattoos. He may be the first person to receive a machine tattoo. Goupille's tattoo is just a simple circle; the machine isn't ready yet to do a full back piece with a unicorn jumping over a Care Bear.
The 3D printer tattoo machine came about during a workshop in Paris organized by the French Ministry of Culture and held at a design school. It all started with a desktop MakerBot 3D printer modified to trace designs onto skin using a pen.
The design students responsible for the mod, who call themselves "appropriate audiences," took it to the next step and mounted a tattoo gun into the machine. After tests on artificial skin, they sought a volunteer to receive an actual tattoo. One of the challenges was sorting out how to make the skin taut enough to receive the tattoo. They settled on using an innertube with a hole cut into it where the tattoo would go.
The machine's first experiment with tattooing a real person was supervised by tattoo professionals, but there are issues surrounding turning a 3D printer into a robotic tattooist. One is sanitation. My human tattoo artist spends a considerable amount of time making sure he, his equipment, and the surroundings are completely clean and in keeping with proper sanitation procedures. A person knows when to let up, when to give you a break. A machine just goes until it's told to stop.
These aren't insurmountable issues for machine tattooing, but they're important to bring up during the early stages of the technology's development.
Details on building the tattoo machine are available on Instructables. Perhaps the instructions to "Start the motor, cross your fingers and...GO!" might make you feel a little nervous. If that's the case, then you should probably stick with human tattoo artists for the time being.