There's a few things that will help you get into a good apprenticeship, as opposed to learning the wrong way.
One thing to consider is that this is a way of life, not just some neat thing that makes you feel cool. Tattooing permeates every aspect of your life, you breathe it, drink it, dream it, live by it and die by it. While it's pretty romanticized these days with all the t.v. shows, the reality is that it is a BEYOND FULL TIME JOB. You don't just show up "9-5" you work all day, then go home and draw, or paint, or market. You get up and get things ready for the days tattoos, if there's no appointments you go market. There are no real days off, even when you have a day off, you're still working somehow.
With that in mind the things that will do you the best are these.
1) Draw, paint, sculpt, whatever you enjoy artistically now, focus all of your time and energy into it.
2) If you aren't taking any art courses now, start to. The more you know about art, composition, color theory, technique, design, typography, etc the better. Every type of art you do influences, and improves each other. Whether it's painting, digital, charcoal, pastel, watercolor, photography, sculpture, or even metalsmithing. It all interacts, as well as prepares you for new art forms you may discover in the future.
3) Put together a portfolio, well made. Don't just throw some pics into a binder, put it together in a professional manner.
4) When you go into a shop looking for an apprenticeship, go in like you are applying for a job, this is after all a life long career. Don't wander in after a day of running around, but pick a day that is dedicated to going into shops looking for your way into the industry.
5) Get to be known at a few shops, if you're a familiar face, and they know that you're an artist, you stand a better chance at being offered a chance. But don't just go in and hang out, get tattooed when you can. No one wants to take on an apprentice with no tattoos. If you don't have good tattoos, how can anyone expect to believe you love it? Also don't just pick shops at random to become familiar, go to a few shops and see where you feel the most comfortable and stoked to visit. If this is hopefully going to be a place that you begin tattooing from you'd better get along with the people who will possibly be teaching and working with you.