I tell my students, "You only need 3 things at the pool at this point. 1. Mask 2. Snorkel 3. Weight belt with weight." At this point, I do overweight my students.
At no point will we leave the shallow end of the pool and I stay between my students and the deep end.
We take our snorkels off our masks and put on our weight belts. Leaving the masks on the pool deck, put on our weight belts, take our snorkels and get into the shallow end of the pool. I keep them no deeper than chest level, waist deep is even better. We put our snorkels in our mouths and breathe from it. I tell them they are learning to breathe through a snorkel. Now that's obviously silly, but I am training them to be comfortable with a mouthpiece in their mouths for long periods of time. I require them to keep the snorkel in their mouth except when the have to take it out to accomplish a particular task. I explain everything first, then I demonstrate the skill, then I give them tips on how to complete the task. Finally, they do the skill. They do it over and over until they think it is easy.
I always teach with simple J snorkels. It can be hard to find them, I keep supply on hand and give them a snorkel with their class. Purge valves and devices to keep water out are unnecessary and a crutch,
I first show them how to breathe through a flooded snorkel. Dipping the snorkel into the water, I hold it up and show (clear J) them the tube is completely blocked with water. I then inhale through the snorkel, bubbling air through the water. Once I have a good breath, I blast the water out of the snorkel. I then have them do the skill.
The second skill involves misdirection. I have them bend over and breathe through theirr snorkels while dipping their faces into the water. If they are comfortable, they stay awhile until they feel natural. If they have difficulty, I tell them to think about drinking through a straw while they practice the excercise. I tell them to remember, they can always stand up to end the excercise at any time. If they need to, they can slowly build up their time until they feel comfortable. They think they are learning a very easy skill - breathing through a snorkel. What they are really learning is no mask breathing. This is a skill that many experienced divers have not mastered. Following this method, your students will master the skill on the very first pool session.
Next, practice dropping underwater, allowing the snorkel to flood and coming up to blast it clear, leaving their face in the water. Continue until they are comfortable.
Finally, we drop our snorkels to the bottom, drop down, put it in our mouths, come up and blast it clear.
At this point, you have accomplished three important things.
1. You lowered their anxiety level by working in a no risk (shallow) environment.
2. Your students became experts in no mask breathing.
3. Your students know they can breathe with a flooded mask.
Now, put your snorkels down and pick up your masks. Tell your students to put it on and drop down to their knees. (Don't forget you explain and demonstrate before having your students attempt any skill) They will then break the seal just enough to allow a small amount of water in. Clear the mask. Do not pull out on the bottom, merely push in on the top while looking up. The biggest mistake most people make is not looking up. The second most common mistake people make is not exhaling through their nose. They must keep their mouths closed. Repeat this until they are comfortable. Don't forget to have them stand up and catch their breath between clearings. Now, increase the amount of water they allow into the mask to about ¼ flooded. When they are comfortable with that level, move to ½, then to a fully flooded mask. When you've reached the point they can clear it easily every time, see how many times they can clear it on one breath. I demonstrate clearing my mask 6 times on one breath. My students all reach at least three times before I move on. After you are at this point, clearing their masks will be easy. You will have reached it in a step by step manner that was easy to accomplish.
Now we drop the mask, put it on, clear it and come up. Finally, put the snorkel on the mask, drop it, recover it, clear the mask, come up and blast clear the snorkel. Remind them that they've just cleared their mask three times on one breath and that this exercise is much easier.
I've found this method to be very effective.