The Red Cross offers swim lessons for adults in many locations.
I recall from another thread that you are a fellow fat person, and the good news is this is actually a good advantage in learning to swim. You will have a lot of natural buoyancy!
My husband (who is very fit) and I sometimes race each other in the pool, and I absolutely give him a run for his money. He has to expend a lot of energy just to avoid sinking like a rock. It's a really fun and heartening form of exercise for a fat person! :-)
Yes! I can beat my husband in swimming, though he has a decent stroke technique and is twice as large and more fit than I am, b/c he is so densely built. His natural float point is about 6 inches below the surface of the water. And there are plenty of very skilled, overweight swimmers at our pool.
OP, I would also recommend trying to take basic lessons from a certified instructor. Once you have the basic stroke down, there are ways to keep yourself on track to make sure your technique stays good (poor technique seems to lead to shoulder pain in many people).
The biggest hurdle is getting comfortable breathing to the side during crawl. Some of this is practice and some is proper technique, which involves keeping your head in more of a straight line with your spine (the natural urge is to tilt your chin up and look more forward and raise your head a bit out of the water, which throws the whole stroke off).
Then you imagine your body rotating from side to side on a spit, while being pulled through the water from the the top of the forehead. Ask your instructor to help you learn this rotation b/c doing it properly will help you breath more easily and position you automatically for better arm technique. I was a successful competitive swimmer as a kid/teenager, and I still needed to work on rotation when I took swimming up as a middle aged adult.
The final crucial point for crawl is to train yourself to reach straight forward from your shoulder, not toward the midline, and to enter the water with your palm down. Then you pull straight down your side with a slightly bent arm. Older techniques (which involved reaching toward the midline, entering thumb down, and doing an s-shaped pull) put way too much pressure on the shoulder. I get shoulder impingement and pain within days if use the 'old' technique.
All of these points are easy to practice, once you get the basics down. And they make a huge difference in speed, ease, and efficiency for aerobic conditioning and calorie burning while preventing injury.
Swimming is awesome. I would be in so much worse shape without it.