First off: Do not be afraid to ask! Most, if not all, seasoned swimmers will very gladly give you a tip or two for a number of reasons...
1. Swimmers, being for the most part, a solitary group of athletes - very rarely receive feedback on how well we're doing until someone asks us how to do a certain turn, or how we manage to swim for so long without breaking, or how is it that we manage to seemingly swim so fast.
2. Swimmers, just like everyone else on the planet, respond to compliments. When you ask a swimmer for advice, this tells them indirectly that you have recognized that they swim well. Would you ask another struggling swimmer how to swim? Of course not. Quite an obvious concept, if you think about it.
3. We've all been there. No matter if you were taught formally by an instructor, or by a friend; we've all had to start somewhere and were taught by someone.
4. Swimming is a very meditative and relaxing type of sport, and most swimmers are a fairly laid back and responsive group of people.
So, let me start with the basics. Don't judge yourself by competing with advanced swimmers. You're doomed to fail, and this will destroy your confidence. Also, I suggest you learn in a pool that is primarily "for lap use only", and not one that has a great number of sun bathers around to make you feel self conscious. Nobody wants an audience around when they are trying to learn something new; and especially if you are learning at an older age. But do know, that there is nothing wrong with how old you are when you start. For example: I couldn't tell you anything about playing the cello, and I'm certainly not much of a piano player; but this doesn't mean I'm stupid. Catch my drift? No pun intended.
The Basics:
Equipment You simply must start with a buoy held firmly, high in between your legs. At first, this may seem like 'training wheels' but they are not. However, they do allow you to hold your core above water. Yet, advanced swimmers use them without kicking: which works the upper body and is an excellent workout to tone and strengthen your arms and back.
You should always wear a swim cap, and I recommend a silicone cap, rather than the more flimsy latex caps in order to protect your hair from the damaging effects of chlorine. And this is especially pertinent if you color your hair, or if you suffer from thinning hair. Chlorine can even damage your eyelashes, but this is only after years and years of excessive swimming. Also, it is a must to shower before you get into a public pool, to prevent infecting others with, well..you know. And it also prevents yourself from being infected by your own unclean body parts. Also, you must wet your hair in non chlorinated water before you put your cap on. Dry hair is like a sponge, and the cap does not provide 100% protection from chlorine.
Goggles are a must. You simply must see under water, and you can't do this in a chlorinated pool against resistance. I recommend a strong set that is flexible, but also provides for a tight enough fit that does not allow water to seep through whilst you swim. And don't be surprised when you find that you frequently need to buy a new set of goggles until you find the right type that works for you. This will just have to be a trial and error process for you.
You could invest in a kick board, or some fins - but I don't find them necessary. Fins are important if you are swimming in an ocean, or a deep lake, but not usually in a pool that is for the most part, "light water".
Lastly, you must buy yourself some flip flops that are made for public pools. And you must
never, ever touch any aspect of a public shower floor with your bare feet. It is extraordinarily easy to catch a nasty nail fungus or athlete's foot, but it is very difficult to recover from them.
Swimsuits are an implied necessity. Just make sure that you are wearing one that you feel confident in. At this point, I wouldn't worry about how your swimsuit might enhance your speed. You'll get to that later.
Breathing Now that you are ready to get into the pool and start swimming, you must not be anxious about breathing under water. This is probably the number one reason why non swimmers don't even try to swim. You need to relax. I can't emphasize relaxation enough to beginners. Start by learning how to blow out ( exhale ) with your nose under water, and breathe in (inhale) by turning your head over the water, and by balancing these two processes until you can obtain your best rhythm. Some swimmers, breathe ( inhale) on every stroke, whilst others ( including me) prefer to turn my head above the water and inhale with every other stroke. Only you can determine which best suits you. I recommend, thinking to yourself a particular relaxing song such as: ( and don't laugh ) " Easy Like Sunday Morning" to get your cadence and breathing/anxiety under control. Eventually, you will learn that you can even cough ( if you must) underwater. Have you ever tried to clear your throat with your mouth closed? Trust me, you can. But this will take time.