Why don't you just go around to any local tattoo place and ask? I seriously doubt they'll be offended, the worst that will happen is you'll be told they aren't interested.
For payment, that's probably going to be variable by place, if you get it at all. Apprenticeships are often unpaid.
Contract is going to vary, too, but most likely it will require you to work there for a certain period of time to repay your training. In some places, you have to be working in a licensed tattoo place to be able to tattoo legally, and that would cover that, so it's good for you, too. Pretty much a contract just says what obligations each party has to the other. Just read over it carefully and ask questions if you have them.