The bible of English phonetics is “Sound Foundations” by Adrian Underhill. This book will cover most of what you and your students need to know. In my early days teaching, I attended a seminar given by Adrian Underhill and he managed to teach us the entire phonetic chart in under an hour. I don’t know whether a video of this has ever been produced. If so, try to get hold of it; his methods for teaching phonetics are excellent and very memorable.
You don’t say whether you are teaching a course that only includes phonetics or whether phonetics are just one part of the course; so the following suggestions might or might not apply to your situation.
work on phonetics regularly;
use short activities on a regular basis. Mark Hancock’s Pronunciation Games has some good activities;
Students should listen to sounds before being asked to produce them themselves;
Whenever you present new language, work on its pronunciation;
After working on sounds, remember to correct students’ errors as you would with any other errors.
As for teaching phonetic symbols, start with the symbols for the sounds that your students find difficult to pronounce. I suggest you consult a copy of Learner English by Michael Swan. He gives very comprehensive coverage of problems encountered by speakers of various languages. If you cannot get hold of a copy, I suggest you speak to some people who have been teaching in your particular setting for some time and ask them which sounds the students find difficult. You’ll also notice it yourself in the first few lessons with your students.
If you would like further information, please write in again giving more information about the classes you are teaching.