Teach each type of vibrato from the easiest to the most difficult. Each type is valid, but the hand vibrato is the easiest to teach, followed by jaw vibrato and the airstream.
Instruct the student to play a pitch that is in the middle of his range and uses no valves. Bb in the middle of the staff or G on the second line are both good options.
Advise the student to play a hand vibrato by holding a pitch and rock the instrument up and down at a slow rate of one cycle per second. Ensure that he is getting a steady and smooth rocking motion. Have him practice this technique on several notes once the technique becomes comfortable.
Prepare the student to play a jaw vibrato by telling him to make a steady chewing motion with his mouth. Once he gets a steady motion going, ask him to play the same note from Step 3, and then move on to several other notes.
Discuss the instructions for playing vibrato with the airstream. Inform the student to use the muscles in his diaphragm to pulse the airstream at about one pulsation per second. Once he can do this without the instrument, have him play the same notes from previous steps.