Becoming a Tattoo Artist
The recent popularity of the tattoo industry has caused a new interest in the career aspect of being a tattoo artist. The potential to make a mark in this artistic field and make a good living from a rewarding career like tattooing is now possible to more individuals. At one time, an apprenticeship was the only path to a career as a tattoo artist. Now there are other options available to people with the money and means.
The most important thing to have is some artistic talent. It's possible to
become a decent tattoo artist without this natural talent but you'll never
become an exceptional artist unless you are artistic to begin with.
Practice your artwork, draw popular tattoo designs.
Hone your artistic talents and skills and start working on a possible portfolio.
Fill your portfolio with a nice variety of pieces to show to potential shop owners. 
Once you feel your portfolio is looking good, you will probably want to hit the pavement and look for an apprenticeship. An apprenticeship is similar to an internship. You'll be working for tips, doing a lot of watching, cleaning of the shop, preparing areas for tattooing, sterilizing equipment and soaking up anything the artists are willing to share with you. This choice is financially hard for most people. Unless you are independently wealthy, or living with your parents, surviving on tips just won't work.

If you do get an apprenticeship, get a contract with the artist you are apprenticing with. This is a good idea for both parties so no one is confused on the terms and you know what to expect at the end of the term.
These days, there is also the option of tattoo schools. These are becoming more popular and available to people. For those of us who would find it impossible to just drop out and work for free, a school may be the answer.
Learning how to become a tattoo artist is like many other professions, it's never really over. As time goes on, you'll learn new techniques and processes from employers, co-workers, workshops, conventions and even employees. You should always be open to learning and developing your skill.
Tattoo Trade Schools
Tattoo Learning Center - Located in NY | World's Only Tattoo School