The first and most important thing to do when you are trying to teach someone to swim is to overcome any fears or apprehensions that they have of the water. Your first lesson or even your first few lessons will be spent doing this. Ease your child into the water slowly, going at their pace. Some children will only want to initially put a toe in the pool while others will want to cannonball off into the deep end.
Once you get children into the water have them hold onto the sides of the pool in the shallow end. The next goal that you have is for them to be comfortable blowing bubbles in the water. Some ways that you work on this with children is to chant the rhyme "Motor boat, motor boat go so slow, motor boat, motor boat go so fast, motor boat, motor Bboat step on the gas..." Then have children blow bubbles in the water.
Going a little bit deeper into the water you next want children to put their face into the water. One great way that you can do this with them is to hold up a number of fingers under the water and have students dip their faces under the water and tell you what number it is that you are holding up.
Still holding onto the side of the wall you need to next teach your students the proper techniques for kicking. You want them to kick from the hip not from the knees. Encourage them to not splash above the water but make ripples under the water. They want to learn the proper kicking technique so that they preserve energy when they are swimming. Holding onto the wall is a great and safe way to help them perfect this technique, you can also have students practice blowing bubbles at the same time.
Once students are getting more comfortable kicking on the wall you can introduce a kick board, which is a floating foam board that students can hold onto to keep them afloat while they are kicking their legs and moving across the pool. As you begin to work with the kick board students will first want to grasp the board tightly as the kick out to you. (Stand about 6 feet from them, so that you can reach them quickly if they panic.) However, as you continue to work encourage them to hold the kick board farther from their bodies and learn to float and balance their bodies in the water.
As students gain confidence and skills with the kickboard, introduce the arm movements to new swimmers. You will want to teach the crawl stroke to begin with because it is the most natural and the most effective. Tell them to picture a windmill, have arms at their sides like a solider and then one at a time run their thumb side of their hand up the side of their body until they are in a chicken pose then their arm comes up over their head and slices through the water with their hands cupped to slice through the water. You can introduce this arm movement to them on the ground before they try it in the water.
Let children try to put the legs and the arms together in the water, do not worry about their breathing rhythms at this point. Help them gain confidence and strength in the water by having them swim different lengths, with you within an arms reach at all times.
The other vital swimming skill that you will want to teach children is to safely swim underwater. You can do this very simply by introducing a hula hoop into your lessons. Have them lean forward and push off of the wall and swim with their face in the water through the hoop. As they get more and more comfortable lower the hula hoop lower and lower into the water until it is resting on the bottom of the shallow end. You can also use diving rings and sticks to encourage students to dive towards the bottom of the pool and safely swim underwater.
As children get better and more comfortable in the water you can introduce other strokes and movements, but these are the important ones to keep children safe around the water.