Purchase a chemical germicide that is recommended for use with tattoo equipment and is known to destroy bacteria and viruses that cause infections in humans. See Resources for links to some such germicides.
Submerge your tattoo equipment completely in a glass container filled with the chemical germicide.
Allow the tattoo equipment to sit in the chemical bath for the amount of time recommended by the germicide's instructions. The time required for sterilization to be achieved will depend on the particular brand of chemical germicide you purchased. Make sure to read the instructions carefully, and be sure to wear protective gloves and goggles when handling potentially dangerous chemicals.
Remove the tattoo equipment of the chemical bath after the designated amount of time has passed. Make sure to remove the equipment using sterile latex gloves, so that you do not recontaminate them. Now your tattoo equipment is sterile and ready to be safely used on your next willing customer.