To become a licensed tattoo artist, you will need to satisfy the terms of the licensing in your state or locality. Usually this requires attending a tattoo school or earning an apprenticeship, and taking a test for the license.
There are some tattoo schools out there, but I haven't heard a lot to recommend them, especially compared to the skills you will learn during an apprenticeship. A school can teach you how to transfer the designs of tattoos in your mind on or paper to ink on human skin, using the correct equipment.
You will learn this and much more during a good apprenticeship. When you've found a licensed, experienced and accomplished artist to take you on and train you, you will learn, over a period of a year or even two or three, how to transform a theoretical tattoo drawn on paper into an actual tattoo. In an apprenticeship, you will also learn the proper use and cleaning of the tattoo equipment. You will learn about inks, how to blend them, how long they last, and so on. There is more to the tattoo business than creating the art, however. You will need to learn good customer service and even the economics of the business.
You may not need a license at all. It depends on your state or local laws. Many require that tattoo artists be certified in how to deal with blood-borne pathogens, but not all do. You need to look into the legal requirements where you live or plan to operate as a tattoo artist. For more information on this, you can also read our section on tattoo laws.