Everyone learns differently, and learning to tattoo is no different. There are several books on tattooing, such as the Huck Spaulding A-Z etc but these can only give you theory and understanding. Tattooing is something that comes through practice and having someone experienced behind you to correct you as you go. Starting out tattooing means you are on the bottom of the food chain and you will learn through long hours of hard work as with any worthwhile career choice. If you have been given the gift of an apprenticeship appreciate it as you have been weeded out from literally hundreds of people who think it would be “cool” to be a tattoo artist.
Learning to tattoo starts out with learning to draw. Sure you may be able to draw a tree, you've always drawn trees, but what about a pig, a pink bow, a dragon riding a unicycle? You have to be able to draw anything at the drop of a hat because you never know what a client will ask for. Down the line you might specialize but until you do you will draw whatever walks in. Drawing a circle and a straight line freehand are probably the hardest tasks you will ever do, coupled with then learning to draw them on a squishy and 3d surface that might move with a vibrating 2lb machine pulling you back. It's daunting at first. Once you have these on paper you might be able to do them on another medium, tattooing pig skin, pumpkins, and drawing on skin with sharpie are just a few of the training tools you might experience. Once you move up to people you start with free work, often on friends and family, and these are the basics of your future clientele. Often you'll start with simple designs like kanji or names and it can take years to build up to a level of portraits and cover up designs.
How your mentor will teach you is entirely up to them, this can either be based on your strengths or how they themselves were taught. The more old school the artist the tougher the apprenticeship experience is likely to be, and the more likely you are to experience hazing. Hazing sadly is a part of most tattoo shops, it's intended as good sport but as the person learning you will undoubtedly have the lions share of the jokes. Some of these are to help you learn, if you screw up you're punished. They are also a weeding out process, if you can't stand up to the pressure then you will quit, meaning you weren't up to being an artist. The important thing is to be aware if you are being taken advantage of. If your mentor keeps asking you to clean up after them but never critiques your drawing or actually shows you anything relating to the job you may simply be there to act as their assistant and they have no intention of teaching you.