You don't need to go deep to practice the basics of snorkeling.
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When you're ready to experience the wonders under the sea, snorkeling is one way to do it. Much simpler than SCUBA diving, snorkeling is something you can do in nearly any body of water, and it requires only minimal equipment. While being a strong swimmer is not absolutely essential, being able to swim well will mean you'll have a much richer experience and be able to see more of what's underneath the surface. Since everyone's skills and confidence levels are different, the only real way to know how you're going to fare is to try it.
The basic snorkeling setup includes a mask for your eyes, a pair of fins for your feet and a snorkel, which is essentially a breathing tube that you hold in your mouth and attaches to your mask so that the open end stays well above the surface of the water. Once you have all of the pieces in place, it's time to get in the water. Start out in shallow water no deeper than chest-height, ideally in an area that stays fairly shallow across a wide area. Before putting your face into the water, put the snorkel in your mouth and breathe in and out a few times so that you get used to breathing through your mouth.
Hit the Water
Once you're somewhat used to the breathing pattern, dip your face in the water and practice breathing while your mouth and nose are submerged, allowing the breathing tube's open end to stay above the surface of the water. If water is seeping into your mask, adjust its tightness by pulling on the straps. Alternatively, get a different sized mask. If water gets into the tube, exhale with force to "clear" it.
When breathing underwater is comfortable for you, lift your feet off the sea floor and practice floating face-down. Snorkel fins float, so when you wear them you'll find that it's even a bit easier to stay in that floating position. When you're confident with your float, try kicking your legs gently to propel yourself forward in the water, either keeping your arms at your sides or moving them in a gentle swim stroke. The fins will be to your advantage here, helping you move faster in the water than you would without them. If you make it this far without incident, you should have some level of confidence that you can actually snorkel without having to be an extremely strong swimmer.
At this point, you can already call yourself a bona fide snorkeler. If you're not confident going into deeper water, it's perfectly OK for you to remain in chest or shoulder-deep water and snorkel to your heart's content. In some places, you'll be able to see schools of fish, coral and other sea treasures right from that shallow position. Just take care in any areas that involve coral reefs. If you need to stand up to catch your breath or reorient yourself, avoid stepping onto the reefs with your fins or bare feet, as the coral could hurt your feet, and you could damage the reef simply by stepping on it. Whenever possible, stand only on sand.
If you're planning to go out on a dive boat or a snorkeling adventure somewhere in deeper water, you'll need to take some precautions to ensure your safety. The first and most obvious is wearing a life vest while you snorkel, which will help you stay afloat in most situations. Just make sure the vest you use is rated for your body weight and that it includes a safety strap to keep it in place if you happen to get rolled around by waves. Also let any dive instructors or group leaders know about your swimming level and never swim alone.