Grab onto the side of the pool at the shallow end with both hands. You should be perpendicular to the edge. Extend your arms out fully -- hang onto the edge with your fingers and not your palms -- and bring yourself into an almost front-floating position. Keep your face out of the water.
Start doing a gentle flutter kick. Keep your legs extended and start to kick your legs up and down. Don’t create too much of a splash; this makes the kicking inefficient.
Sweep one arm, fingers closed, down into the water. Bring your hand and arm out of the water and above your head to complete a circle. Keep your elbow slightly bent as it goes down into the water, but bend it more when it’s overhead -- keep the stroke gentle and bend your arm enough so that you don’t feel awkward strain. Place your hand back on the pool edge. Repeat with your other arm. You should be pushing water toward your feet with your hands, so keep those fingers together the entire time. Do this over and over, slowly, until you get used to the motion of circling your arms while kicking. Be aware of your fingers -- don’t crash them into the pool edge.
Hold onto the edge with both hands, take a breath and put your face in the water. Don’t plunge it in; lower it until your forehead is completely in the water. (Ref 1) As you continue to kick, breathe out through your nose, and then turn your face to one side so that your nose and mouth are out of the water. Inhale through your mouth. Turn your face back down into the water while holding your breath. Never keep your face submerged for longer than is comfortable. Turn your head and breathe whenever you need to or want to. Repeat this on the other side, and alternate sides until you get more comfortable with the hold/exhale/turn/inhale/hold process.
Combine Steps 3 and 4 by slowly circling your arms as you turn your face to the side. Turn to the side with the upraised arm when it is passing above your head. Do not turn your head to the side with the arm that’s still holding onto the pool edge. Repeat this, alternating arms, until you are able to coordinate your breathing with your arm movement. Again, be aware of where your fingers are relative to the pool edge as you bring your arm down.
Stand up, let go of the pool edge and turn so you’re parallel with the edge. Now you’re going to repeat the arm and breathing motions without a pool edge in your way. Move into water that’s just deep enough so that you don’t have to bend too far forward to do this, but stay out of water that makes you stand on your toes to keep your head above the surface.
Start circling your arms, but instead of starting one circle right as you finish the other, cycle them. Have one arm pushing down into the water as your other arm is overhead. When one arm is stretched out in front of you, the other should be stretched toward your back. When you’ve got that memorized, bend forward a bit so you can put your face in the water. Hold your breath, submerge your face, start moving your arms, exhale through your nose and turn your face to one side when the arm on that side is passing over your head. Alternate sides. It’s crucial that you get this coordination down so that you don’t inhale water when you swim.
Put on a flotation device and put the moves together. Take a deep breath and hold it. Lean forward into a front-float position and start circling your arms and kicking. You can keep your face out of the water for a bit if you don’t want to add in the breathing yet, but be aware that this will make the stroke seem a bit tougher. But if you are adding in the breathing, remember to turn your face to the side, high enough to get your nose and mouth out of the water, when that arm is passing over your head. Eventually you’ll be able to try this without a flotation device, but keep the flotation device on until you’re able to really move around the pool comfortably.