How do they do tattoos in prison?

They get a sewing needle, dip it in ink and then stab where they want to make the mark.

The methods used within prison are varied of course but those methods are generally broke down into two primary tasks. The first is manufacture of the ink. This is usually accomplished by burning a baby oil lamp and collecting the soot (known as lamp black) within a paper bag or cardboard box. The lamp black is then scraped out and mixed with shampoo. Since shampoo is a detergent the particulates stay suspended well within the mixture. The inmates will often put some rocks in the bottle that contains this ink to help mix it up when it is shaken. Sometimes plastic with be burned instead of baby oil to make the soot. The next primary task is making the tattoo gun. These are usually made from motors scrounged from cassette tape players or CD players. A "barrel" made from a cut off piece of a ball point pen is attached to the motor and a sharpened piece of guitar wire is threaded through the pen tube and attached to the motor shaft. Attach some batteries and the rig is ready tattoo! The tip of the wire is dipped in the ink which is usually put in a toothpaste tube cap. Other paraphernalia used are stencils of art paper used for the pattern etc....