Depending on the accessible materials they basically forge a tattoo gun and harvest ink.
Ink is most commonly made from soot. Pieces of plastic (from a chess or checkers set) are melted in a confined area, a piece of paper is held above the burning plastic to collect the soot. The soot is then scraped off and mixed with lotion or baby oil. Thus creating your ink.
Needles are made from the spring inside a pen. The spring is unraveled and sharpened, then wrapped with thread to hold ink.