I fully understand and sympathise with your situation. It is unusual, but not unknown, to teach children in a one-to-one setting. I always think it’s a shame because children are shy when they are alone with their teachers; they get a lot of their energy from being with other children which can make a lesson with just one child hard work at the beginning. Having said that, your first task will be to build up a good working relationship with the child.
As for your question about the course book; I definitely recommend that you use one. It will give structure to the course and will help you to plan your lessons. You shouldn’t be re-inventing the wheel for every lesson. By using a course book, you have the outline for your lessons and can follow the activities exactly, adapt them to suit the child and level or even leave them out. You should speak to somebody at the school to get help choosing a course book. You don’t mention the age or level of your students, so I can’t recommend a book to you. I suggest that you don’t buy the book for the first lesson. During the first few lessons, take activities from various sources to see which books and levels are best suited to the student. Always check on copyright before photocopying.
I would not recommend that you give the level test to do as homework. Well-intentioned parents often help their children complete the test, believing that they are doing a favour. In reality, this only serves to skew your judgement re the level of the student and the first few lessons will then be spent working on material that may be at the wrong level. I suggest you give the test during the first lesson (45 minutes) and do a speaking activity or game for the rest of the time. That will help with your question about planning for the first lesson. By the time you go into the second lesson, you will have an idea of the student’s level.
As for games, I know what you mean. Most games are aimed at large classes. You could play memory games such as Kim’s game: allow the student to look at 8 objects for one minute. Then hide the objects; the student names as many as possible in a set timeframe. You could play a game of snap with cards that have pictures of objects on them. When you see two cards with the same object, instead of calling out “snap”, call out the name of the object to win the cards. Play “Am I lying?” this is an idea taken from “Recipes for Tired Teachers”. Children of all ages and teenagers love this game. You can see a description of the game here:viewtopic.php?f=2&t=602
I hope all of this will help you through your first lessons. If you would like more ideas, please write in again.