And since we have a pool in our backyard, I can take the whole year to really get her to the point where she can do it herself. Parents Magazine suggests that parents always be within reaching distance of a child learning to swim. Since my child is 4, I trust her, but I would never leave her alone...not even with the floaters on. Our rule is that if I am not within reaching distance, then she must sit on the edge and kick her feet in the water until I get back. This may not work for children who are opposed to listening...trust yourself;know your child.
To get your child comfortable with the water, there are some "games" you can play with him/her. You can teach your child to blow bubbles in the water on the stairs or when swimming with the floaters on. I only use the Stearn's Floater. It buckles around the back and doesn't cause them to tip forward into the water.
You can teach them to dog paddle and to kick with their feet.
Place a toy that sinks on the first step and encourage them to pick it up without having to put their faces in the water.
Learning to go underwater is much harder, especially if you have a fearful child. My child hated it at first. But we made it a competition. I do the 1-2-3 BLASTOFF countdown...she plugs her nose, closes her mouth and her eyes, and we BOTH go under. Teaching means doing together.
Swimming takes time. You can definitely get lessons, but you can do it yourself too!