If your child can put her whole face in the water for at least 10 seconds, float on her front, float on her back, and has mastered various other rolls and floats, then she's ready to learn basic breath-control skills (blowing bubbles).

Don't worry if your child hasn't given up the nose clip yet — she can start by blowing bubbles with her mouth. Ultimately, though, blowing bubbles with her nose is the better choice, since it's more efficient at keeping water out of the nose. If a swimming pool isn't an option, your child can practice this in a bathtub.
Blowing bubbles through the mouth
Before putting her face in the water, have your child practice taking a deep breath in, then exhaling slowly through her mouth. (Don't let her hyperventilate.)
Have her sit in a bathtub or on the steps of a swimming pool. Tell her to hold her breath, place her mouth in the water, and blow bubbles at the surface. Assuming that went well, have her do it again — this time with her whole face or head in the water.
Have fun experimenting. Have an underwater birthday party and blow out the candles on an imaginary cake. You can also have her blow bubbles for a second, then stop, then start again. Or hold her breath for about ten seconds underwater, then blow bubbles slowly until she needs to come up for air. This new skill will let her keep her face in the water longer — many of my students can stay under for twenty to thirty seconds or more.
Blowing bubbles through the nose
Blowing bubbles through the nose can be more challenging for children. Demonstrate first, out of the water: take a deep breath in through your mouth, then exhale forcefully through your nose so your child can hear the air pass through.
Now have her hum after inhaling through her mouth — humming automatically blows air through the nose, and it's easier for young swimmers to grasp than just exhaling. Then try it in the water: take a deep breath in through the mouth, start humming, and place her mouth and nose in the water.
The first few times, the bubbles will probably come from her mouth — stress that she needs to close her mouth tight to make the bubbles come from her nose. It takes more practice, but it's worth it: it's the best way to keep water out of the nose, especially when rolling over. If she exhales (or hums) before her nose hits the water, keeps it up while underwater, and continues until after she's safely emerged, that guarantees a happy nose.
Bobbing
Bobbing is rhythmic breathing while bouncing up and down in the water — essential when learning formal swimming strokes. It's best learned in chest-deep water.
Demonstrate first: take a breath in through your mouth, squat down to submerge your whole head, exhale slowly through your mouth or nose, then come right back up for more air. Repeat rhythmically three or four times.
Now it's your child's turn. If she needs help, hold her on your hip and take her down and up, instructing her each time to take a breath, then blow bubbles. Or face each other and try it while holding hands. With practice — and an even exchange of air in and out — she should eventually be able to do this for a minute or more. At first, start with attainable goals, like three or five bobs in a row.
What's next?
Teach your child to propel through the water, if you haven't already. Otherwise, if there's no trace of fear when she plays in the shallow end, she's ready to be introduced to the deep end.
Want a head start? Get my free course — How to Prepare Your Baby for Swim Lessons (0–8 months).