Q) What is the proper way of obtaining a apprentice ship. when you have no tattoo experience but quality art work.
A) That's the big question, isn't it? I'd like to start out by pointing out that tattooing is an amazing career to have- especially when approached the right way. If you end up with poor skills in a crappy shop, it can be a fairly bleak way to make a living, so you need to start out right. That said, I'd like to lay it on thicker by comparing it to any other career in this pay bracket, which in most cases would require a college education. For higher education, students are expected to relocate and/or go into a decade or more of loan debt just to have a chance at a job that would make them that kind of money. So if you can find a good opportunity to learn from a quality artist at a solid shop, that's worth relocating for, worth borrowing money from your family to live by while going through the apprenticeship stage, which usually will entail a period of months where you make no money at all, yet are expected to be at the shop full-time. Good apprenticeship opportunities are so valuable that you need to be ready to treat it like a rare break and make the necessary sacrifices.
I am not really down with those pay-per apprenticeships, which can run ten grand or more and usually leave you with little more than nominal tattoo skills and a contract stating you won't work within 300 miles of the shop where you learned. If absolutely nothing else comes up, I'm not saying you shouldn't pay to learn, but an ideal situation is one where the shop owner wants to teach you so you can be good enough to work in their shop. You will get a better education from an artist who knows your future success will reflect on them, otherwise they won't make the right investment in you.
If you are in fact a skilled artist, you need to get your portfolio together. In the old days, this meant making 8x10 glossy prints of 10-20 of your best pieces and putting them in a nice view binder with a cover image and an introduction letter. These days this physical portfolio is still helpful but you also need a good online portfolio, presented in a clean and professional way. Show the range and variety of what you are capable of, including drawings that are specifically meant as potential tattoo designs. Keep it short- make the point with as few images as you can, but then maybe include a link for anyone who wants to see more. Most attention spans are short... plus, the first impression will happen while they are viewing the first 2-3 images in your portfolio. Keep that in mind when you put it together, and be prepared to update it regularly as you create new, fresher art. Show your dedication to the art- shop owners won't even bother with a portfolio that looks unfinished. Lazy tattoo artists are a dime a dozen and a pain in the ass to the shop owner, who is trying to keep their doors open. It has to be a good first impression on all levels: Art, presentation, professionalism, thoroughness. Provide a short statement on who you are, what art experience you have and why you think you'll make a great tattooer, plus relevant contact info.
Then it's all about networking- online, at conventions, by looking at classified ads in tattoo magazines. I hear stories from topnotch shop owners who have ads running in magazines for a year at a time without any really serious inquiries. Be that serious one, and you may find yourself a job.
Long story short: it will not be easy or convenient to get started. Be prepared to reconstruct your life around your new career.