Becoming an apprentice isn't easy at all but these things can help. (FYI this is all from my experience so take what you can use, leave the rest behind.
  1. Don't.
    Everyone wants to have what the think is a "cool" job and don't realize the amount of work and commitment it takes to get where you need to be. The market is already flooded with tons of tattooers (many of which deliver sub par work) so if you want a easy way in and don't care about the trade, you're better off finding something else to do.
  2. Get Tattooed (A LOT)
    This one seems pretty straightforward. Why would you want to tattoo without being into the art form for yourself. Getting tattooed helps you see what your future clients will be going through and can help with your bedside manner and grounding. Also if there is someone specific that you want to learn from GET TATTOOED BY THEM! No one likes hiring random people that stop by to "See if you're hiring Apprentices" and it gives your would be mentor and you a chance to get to know each other.
  3. Draw All The Time
    While tattooing is more of trade craft than just an art, it's important to keep practicing. The more you put in the more you get out. Flash and design books (that are quality) help you learn the in's and outs of what makes a good tattoo design wise and help teach basic fundamentals. Also have your drawings critiqued to help build up your strengths and weaknesses.
  4. Have A Thick Skin
    Apprenticing isn't easy in any field. You have to have the attitude that you are working from the bottom to where you want to be. Remember that all the tasks that you think are menial are important and being taught to you for a reason. Keep a positive attitude, remember that you are lucky to be building a new career, and be thankful and humble to those around that are helping you. The right attitude is way more important than any machine or drawing skill you might have.
  5. Be Prepared To Move
    A good apprenticeship is worth it's weight in gold. Not just because of the skills that you'll acquire, but also because of the doors it'll open for you down the road. Don't settle for anything but the best mentor you can find and if you have to move to do it, then do it! Working in a good shop affords more chances to learn, guest spot, and meet new people. While this is all awesome, if you're a dick it doesn't matter what shop you come from.
  6. Be Prepared To Work
    Most apprenticeships are unpaid (some even require you to pay for them, be wary of this) and can last anywhere from 1-3 years. This means you'll be working at the shop and at least one other job to keep a roof over your head. The workload can get nuts but remember that if you bust your ass and keep a good attitude there is a light at the end of the tunnel.
  7. Be Wary of "Tattooer Mills"
    Some shops are "Tattooer Mills" that take an apprentices money (usually in the thousands of dollars), have them work in the shop for a while, and fire them without teaching them anything before finding another apprentice. Not only can this royally fuck you over but it can also hinder your future career. Don't work anywhere you wouldn't get tattooed! A foot in the door to the industry isn't worth a bad apprenticeship.
  8. Save A Lot Of Money
    The initial cost of starting to tattoo can be a bit scary to some. Machines, pigment, needles, tubes, a power supply, a clip cord, etc. can add up to quite a bit of cash fast. But by saving before your apprenticeship starts you can help offset that and take some pressure off yourself. If you can save enough you may not even need a second job.
  9. Buy Quality Supplies
    "Good tattoos aren't cheap. Cheap tattoos aren't good" This maxim holds up for everything in life. You don't have to go out and buy the most expensive items available, but do your research and buy the BEST you can. Investing early helps you save money in the long run by not having to replace things as they fall apart.
  10. Be Patient, Be Humble, Have Fun.
    Good things don't happen overnight but if you put your work in, keep a good attitude, and enjoy the ride!