Don't rush the process. Start slowly by wading in the shallow end and getting used to the water. The Aiken Standard gives some good tips on how to acclimate children into the water that can be applied to adults as well. One of these is to concentrate on activities you are comfortable with.
Learn how to tread water first. Once you can learn how to stay afloat the rest of the skills will come with practice. Use some type of flotation device like a kick board, inner tube or personal flotation device (PDF), in order to get used to the feeling of floating. Treading water is basically flailing with your arms and kicking with your legs while being perpendicular in the water (watch the Youtube video to see the technique).
Learn how to float on your back and front. Another emergency swimming technique is floating. It can keep you upright without using the same amount of energy as floating. The first thing you need to do is to learn to relax, according to an article by iSport.com. Use a flotation device first and then take it away and see if you can stay afloat on your back. Breathe deeply and look at the sky. Press your weight on your shoulder blades and lean your head back as if on a pillow. If your legs sink, then place your arms above your head to create more balance. Kick your legs very gently and thrust your stomach up in the water to maintain flotation.
Become comfortable with holding your breath and swimming underwater. Swim-teach recommends going slowly as this is the most terrifying aspect of learning for most. Splash water on your face first. Then go halfway down in the water until you feel comfortable for complete submersion. This is a technique, which can also be practiced in the bath tub at home. At the same time, improve the ability to hold your breath by practicing this as well. Time how long you can go without taking a breath with a stop watch.
Sign up for a local class at the park district. Speak with the tutor or the instructor and make sure they will meet your needs. If you are hydrophobic, there are sometimes swimming classes where the class is geared towards meeting these fears. These programs function as workshops and simultaneously ease people of the fear of water through programs combined with actual instruction in the water.