Find a place where you know the precise depth of the water at all times. In most swimming pools, the depth is clearly marked along the edge, but in a natural body of water, you may have to investigate more cautiously, using a stick or an experienced swimmer. It is important to remain in water where you can touch the bottom and still keep your head above the surface until you teach yourself how to swim.
Teach yourself how to swim by learning how to tread water, making sure that you venture into a pool depth that is deep enough so that your feet won't hit the bottom, but not too deep that you won't be able to rest safely. Treading water involves kicking your legs gently while floating in a vertical position, like riding a bicycle. Practice this until you can keep your head afloat for 20 to 30 seconds at a time.
Practice floating on your back by holding a deep breath and allowing your body to become buoyant in the water. This will teach you to stay afloat when you become too tired to swim, and will help to reduce your fears of the water.
Grab an edge on the side of the pool and allow your body to float to the surface by taking another deep breath, this time on your stomach. Once your body becomes close to horizontal in the water, start kicking gently, alternating the motion of your feet. Practice staying afloat this way until you can manage 20 to 30 seconds at a time as well.
Start developing the proper arm strokes by pushing off the side of the pool, taking a deep breath and starting your kicking motion. Your arm strokes should be smooth and centered well below the surface of the water, which will propel you forward. Experiment with the various types of swimming strokes, and practice swimming longer distances.