I’m currently employed as a tutor where I attend college, and since I’ve been having students heaped onto me (not literally, thank Og), I figure I’m doing something right:)
You exist, for one, to become obsolete. Your goal, as with most of the service industry, is for your customer/client/student/etc. to no longer need your services.
Try as much as possible to avoid telling him things outright, unless it’s clear he’s not going to understand them without direct assistance. You’re merely guiding him in the direction of the answer. Once he sees it, stay out of the way so he can figure out things for himself.
When he does get answers right, make sure he knows why they’re right. Make sure, IOW, that he understands the mechanisms - if x-7=12, x=19, but can he work the problem from multiple angles? If so, he understands how to add/subtract from both sides and how to isolate a variable. But if he only does x+y=z problems instead of, say, 2x=y-z, then he’s not going to be able to apply what he’s learning to different, more difficult problems.
Emphasize what he gets right. Students of all ages hate to see tutor sessions as time spent looking at all their mistakes. If he sees the progress he’s making, he’s more likely to be diligent in his work (or moreso if he already is). Say, for example, “Now, see, last week you would have made a mistake here at this negative sign, or you would have forgotten to distribute this two to both Xs and one of the 5s. You’re doing it perfectly now.” Students often do not see the progress they are making because they are so focused on not making mistakes that they notice only when they make them.
Start from the beginning unless your student shows you that he has progressed past that. Especially do this in a new chapter or when a markedly different concept is involved. With my geometry student, we just spent weeks doing triangles, and we’re now doing quadrilaterals, so we’re not going as fast as we were because there’s drastically new material to be covered. However, she understands the material, so we won’t later discover that sections 4.1-4.3 completely eluded her (to her surprise), and we won’t have to spend a month learning what we’re doing now.
If you have a student who gets discouraged easily, emphasize to him (if it’s true) that the mistakes and troubles he’s encountering are not unique to him. The biggest problem my English student has is that her self-esteem started out very low. She knew the material, she just had no confidence in her decision-making ability. Once she saw that I had confidence in her, that I cared enough to spend adequate time listening to her and explaining something to her until we both knew she understood it, her brain soared ahead. But for a long time she’s thought she was just dumb, so the knowledge she had was of little use to her because she didn’t trust herself.
If your student is the sort who occasionally needs to break what can be very intense study sessions, don’t be afraid to crack a joke or something like that. In the beginning, with my geometry student, she would get frustrated easily by proofs and especially triangle proofs. So I joked with her a lot about them and got her relaxed and comfortable and understanding that it wasn’t the end of the world if it didn’t come to her right then and there. Once she was able to relax, sessions moved much more smoothly.
Your student should be the one drawing diagrams unless he doesn’t know what to do. In that case, you direct him to wherever the instructions are and just have him read them aloud. If the language is puzzling, state them in a different way or ask him what part he doesn’t understand. You have to be careful how you phrase any questions, though, because he might think you’re asking “Come on, how do you not know this?”. If it’s truly puzzling, explain what you’re doing as you write it and tell him to jump in when he thinks he can take over for you. Once he gets the hang of whatever you two are doing, leave him alone aside from the occasional question, or to point out something he’ll want to pay close attention to. With my math students in general, one thing they often make mistakes in is FOILing (first, outer, inner, last). While I can do it in my head, not everyone can, regardless of how much practice they’ve had, so I make sure to still ask questions about FOILing so they get more accustomed to its nuances (sign changes and such, mostly).
That’s all I can think of for now. If you have more specific questions I’ll be glad to help:)