Factors to evaluate with respect to breathing are:

• Completes exhale underwater
• Quick intake of breath
• Turning of head to inhale is timed and integrated with body roll
• Head is only turned sufficiently to breath
  (facing the side of pool not the ceiling, one eye at least partially submerged)
• Breathing is via a roll to the side not by lifting the head.

Here is Ian Thorpe demonstrating good breathing technique:

Variations: some swimmers prefer to do a continuous slow exhale while they swim while others prefer to exhale the majority of their air just prior to their face clearing the water to inhale. The sudden exhale requires more energy but provides more buoyancy and either style is functional as long as the exhale is completed before the face leaves the water so as to minimize the time the head is rotated for breath and avoid any distruption to the timing of the stroke.

Not completing exhale underwater

Novice swimmers sometimes wait until their face is out of the water before exhaling. This prolongs the period the face must be out of the water which interferes with the timing of the body roll and the rest of the stroke. It is also more energy intensive to quickly exhale and inhale and will tend to make the swimmer tense up.

If the swimmer has not achieved a full exhale they won't be able to inhale fully and will neither clear accumulating CO2 nor take in sufficient oxygen. This is particularly common in races where the swimmer is holding their breath for multiple cycles and may forget to exhale before rotating to inhale.

Getting out of breath even when swimming slow and relaxed is often a symptom of incorrect breathing. In general swimmers should concentrate on exhaling, the inhale will happen naturally.

Breathing is not integrated with the body roll

Novice swimmers, and particularly those with a flat non-rolling style, will perform all sorts of head movements in order to get their mouth to air, including lifting it to the front and flinging it wildly from side to side. With a proper body roll of approximately 45 degrees the head can be smoothly turned the the side a further 45 degrees resulting in a head position facing the side of the pool at which point a quick inhale can be performed and the head can be returned to facing the bottom of the pool.

Excessive rotation of the head

Some swimmers feel the need to get their entire face out of the water to breath and this causes them to overrotate their head and/or their body so that their head is facing the ceiling instead of the side of the pool.

Bad: head facing ceiling, body overrotated

Good: head facing to side, proper body rotation, breathing into the trough of the "bow wave"

Good: head facing to side, one goggle still partly underwater

The most effective video shot for evaluating breathing is an above water tracking shot from the side that is zoomed in on the head and upper body. The video of Ian Thorpe on this page is a good example. A tracking shot from below as in the initial view in the following video of Michael Phelps can allow you to observe the exhale, but is relatively difficult to capture. A non-tracking view from below can work if the timing of the breath coincides with the swimmer passing over the camera.

Video of Michael Phelps' freestyle from various angles

In most cases it will be easier to instruct the swimmer on exhaling than to try to detect a lack of exhale via video.

The most common breathing patterns for continuous swimming are every other arm stroke (always to one side) and every third arm stroke (bilateral breathing to alternating sides). Swimmers who always breath to their left or right side will tend to develop asymetric strokes and are prone to underrotating to their non-breathing side. The ability to breath to both sides, whether via bilateral breathing or via changing the side breathed to every half length or length, is useful in open water swimming and during races, and can help prevent an excessively asymetric stroke.

For shorter distances swimmers may breath less often, possibly not breathing at all in a 50m race.

For long distance swimming speed is limited by aerobic capacity and restricting breathing will limit oxygen. Distance swimmers should be encouraged to be proficient and comfortable breathing every stroke, preferably to either side.

Drills that restrict breathing frequency can help swimmers get used to the discomfort that occurs during racing and allow them to practice overcoming the urge to disrupt their stroke to get additional air. Restricted breathing frequency drills do not "expand lung capacity".