To achieve this most competitive swimmers exhale underwater, leaving themselves only to breathe in once their mouth is above water level. There are two main ways of achieving this, either continuously exhaling in a trickle between breaths (humming can be a useful way of practising this), or by holding one’s breath and then exhaling vigorously just before taking the inward breath. Which method is better will depend on the frequency of breathing (short durations between breaths can often mean there is little difference between the two methods) and personal preference.
The video here shows an example of explosive exhalation between breaths. Note the fast stream of bubbles exiting the swimmer’s nose. In this case the swimmer is breathing every stoke to her right so there is no difference between trickle and explosive exhalation and the bubbles start to appear almost as soon as her face is back in the water. The critical point is that all the air is gone before she takes her next breath.