I completed a BA in Professional Writing (English) from Purdue University in May 2009. I had a 3.4 overall GPA and an English-specific GPA of nearly 4.0. While working on my degree I participated in two large group writing projects in which I learned a lot about writing, on both a practical and a theoretical (or teaching) level. I also took many classes in literature, and even won a prestigious undergraduate award in literary criticism.
I believe very strongly that the best way to learn about writing is to write, to receive feedback, and to write some more. A method similar to this, called "workshopping" is widely used in Purdue classes. For me as a tutor, this means I would want the student to bring me an assignment or assignments he or she needed to work on for school (or I would set an assignment if none were available), and we would discuss it, and revise it together, making sure the student understood the logic and reasoning through each step. Some writing exercises are also fun, like games, and these can be a great way to learn about style, tone, voice, or how to plan a piece before writing it. As a tutor, I would use these exercises to strengthen my pupils' understanding where necessary.
As far as teaching literature or reading is concerned, this is similar to writing. Not only in that the best way to learn to read is to read and then to summarize what you have read, but also in that learning to be a better writer makes you a better reader...and vice versa. In addition to summarizing what you've read in your own words, learning key words and phrases is important to reading quickly and still comprehending what you read, as is necessary in the SAT Reading section.
A study of vocabulary is useful in both reading and writing, and needs to focus on ways to recognize parts of words that will a reader clues as to what the word means and what kind of functions it performs. Vocabulary also requires a lot of memorization and can take time to learn, but it is very rewarding.