Determine the student's level of experience. You can do this by testing his ability to play or sing scales and songs, read sheet music and memorize tunes. It is pointless to teach someone music that they already know, so you must be very exacting when determining the limits of the student's musical ability.
Create an adult-appropriate learning environment. Adults do not like to learn in environments that seem like they were designed for children. A good learning environment for adults should look more like an office than a classroom. Decorate the room with artwork, and keep plenty of musical instruments around to allow free experimentation with musical concepts.
Ask the student what he wants to learn. Adults who take music classes usually have a specific idea of what they want to learn, whether it is a song, an instrument or a composition style. Ask your student what their learning objectives are, and prepare lessons based around those objectives. If your student is not yet at the right level to begin learning the songs he wants to learn, prepare a series of skill lessons that can take him to where he needs to be.
Begin instruction by explaining the relevant principles of music theory. One difference between adult learners and kid learners is that adult learners usually have enough crystallized intelligence to begin the learning process with theoretical material. Kids, who have more fluid intelligence, learn best by starting with hands on instruction. If your student wants to learn to sing, begin by explaining how all vocal melodies on an eight-note scale (or octave.)
Demonstrate techniques by performing them yourself. Show the student what the technique should look like, by singing or playing the piece proficiently more than one time. This will give the student an idea of what to aim for.
Have the student attempt the technique. Break the technique down into small pieces so that the student can master it bit by bit. If the student has literally no experience with the instrument, start by placing their fingers on the keys or strings to show him what he needs to do with his hands. After preparing him like this, have him attempt the technique on his own.
Critique and correct the student's technique. Tell him what he did right and what he did wrong. Perform another demonstration to show him what the technique should look and sound like. Advise him on what do to with his hands (if the lesson involves an instrument) or chest (if the lesson involves singing). This will help the student correct his mistakes.