NOT A LANGUAGE TEACHER
Drama is very easy to do with a group, and would a brilliant way to develop language skills. Drama with one child is a bit of a challenge! Most of the work you do with children is based on games, and playing games with just the two of you needs a bit of imagination.
It will be easier when your pupil has more English, then you can play games such as mimes. In this game, one person mimes an action – start with easy things like painting a wall, smoking a cigarette, licking a lollipop – and the other person has to guess, and say in English, what they are doing. This would help the pupil learn vocabulary, practise pairing verbs and nouns, and learn new verbs and nouns (encourage him to mime actions he can't yet describe in English, to learn them from you).
The progression of this game, once the pupil is very confident with the first stage, is for the first person to mime an action (let's say hammering in a nail), but says they are doing something else (drinking tea). The second person mimes drinking tea, but says they are doing something else. So:
Person 1 Starts the game by miming hammering in a nail, but says I am drinking tea
Person 2 Mimes drinking tea, but says I am stroking a dog
Person 1 Mimes stroking a dog, but says I am playing tennis
Person 2 Mimes playing tennis but says I am brushing my hair
The object is to switch from one person to the other as quickly as possible! It works best in a circle with a number people, but you can do it on a one-to-one basis. It's a warm-up game, to get everyone thinking and reacting as quickly as possible, and might be a nice way to start your lessons once the boy has a bit more vocabulary.
That's one example, anyway. There must be loads of other games that originated in drama classes that you could adapt – if you want to develop it as a teaching strategy, search the net on 'drama games + children' and see what you get.