tatt_bra says:

There are many answers here relating to this. I really like what Tattoopheliac has said a couple of times. As a studio owner, when I view portfolios, I am not interested in looking at tattoo work or flash designs. I want to see art. I am most interested in pen and ink drawings and if you rock out portraits that is a definite plus.
Try to present a professional looking portfolio with a variety of media. Many bring in photos of commissioned work and that is really great. One apprentice we had did bus bench art – it was awesome!
Apprenticeships are very difficult to acquire so you are right, you need to be very committed. We get a lot of email inquiries and even though we generally have an apprentice at the time, we offer to look at the portfolio and give advice. This is always in your best interest to do this if offered.
Expect to pay a few thousand dollars and you will need to likely have a part time job somewhere so you can survive the couple years it takes to do this. In reviewing this, though, you are asking about an apprenticeship but really not saying you want to tattoo, just design. Tattoo artists do their own designing or have their apprentices design for them. Designing alone would not be a job to make any kind of money at as the artist already does a shop split and can’t be paying out anyone else.