Deliberately slowing your breathing shifts your physiology within a couple of minutes. That part is real and measurable. What it will not do is change whatever is causing the stress.
What the evidence shows
Slow-paced breathing at around six breaths a minute reliably increases heart rate variability and reduces measures of sympathetic nervous system activity in controlled studies. Trials of breathing-based interventions for anxiety symptoms show benefit, though the studies are usually small, hard to blind, and mixed in quality. Hence Grade B rather than A.
The immediate physiological effect is better established than the long-term clinical one, and it is worth keeping those apart.
How much difference it makes
In the moment, meaningfully. It is a genuinely useful tool for a spike of acute stress, and it has the rare advantage of being free, portable and impossible to overdose on.
Over months, on its own, for a real anxiety disorder or a genuinely unmanageable workload, it is not sufficient and should not be offered as though it were. Telling someone in a serious situation to breathe more slowly is close to insulting if it is all you offer.
What to do
Breathe in through the nose for about four seconds, out through the mouth for about six. The longer exhale is the part that matters. Continue for two to five minutes.
Practise it when you are calm, so it is available when you are not. A technique first attempted during a panic response usually fails.
Cautions
If you have a respiratory condition, adapt the timings to what is comfortable rather than forcing a pattern. If breathing exercises make you feel worse, which happens for some people with panic symptoms or a trauma history, stop and speak to a professional about approaches that suit you better.
When to see a doctor
Persistent anxiety that interferes with work, sleep or relationships is treatable, and the treatments that work well are talking therapies and, where appropriate, medication. Breathing exercises are a useful addition to those, not a replacement. If you are struggling, please speak to your doctor.