This is by far the most popular meditation method, taught to beginners as the first entrypoint into meditation. But it is not as easy as it is made out to be. It is easy to teach, but not easy to learn. I found myself struggling with this method for many years before it really clicked. Popular descriptions of it are simple, perhaps too simple. For example: “watch the breath go in and out”. But there are subtleties and pitfalls which need to be mentioned and explained, which are lacking in popular teachings.
The core method is this: allow the breath to go wherever it wants to go, at whatever speed it wants to go. Just follow along and watch it, without exerting any force or effort in any direction. Float on the river and let it take you wherever it goes. Surrender control of the breath.
Watch breathing as a natural process - not belonging to you but being a part of nature. Then there is no reason to interfere with the breath, you can just let it be, and just watch silently.
As this open, allowing consciousness of the breath heightens, the breath becomes slow, deep, and calm. This is the clear, tangible feedback that you are doing it correctly. The quality of the breath transforms; it becomes fulfilling, satiating, rejuvenating. There is a deep sense of release and relief, a cool serenity. At the peak of awareness, the breath momentarily becomes completely still. These gaps of stillness are invaluable.
The biggest pitfall of this method is to expect the breath to rise and fall in a fixed rhythm, and thus leading it with a consistent speed and/or magnitude. This is effectively a form of control of the breath, and it prevents the innate meditative quality of the breath from emerging. This kind of controlled breathing often results in mild hyperventilation and has the opposite effect of meditation, where you become less calm and relaxed. You have to let go of the breath, drop all force, and just be an allower and an observer of its natural movement. The breathing is the object of your meditation and you simply allow it to be exactly where it is, and to go wherever it wants to go.
The second pitfall is conflating the breath with emotion. Normally, we expect the breathing to mirror our emotional state: anxiety and distress causes the breath to become short and fast, while being relaxed and happy causes the breath to become slower and deeper. However, it is a two-way relationship: if the breathing changes independently, the emotional state also changes to reflect it. In this method, perceive the breathing separately from the emotion that you feel and the thoughts that you think. The method’s work is only on the physical breath. Thoughts may slow down and emotions may calm down as a side effect, but those are not the main focus of the method. The focus is the physical breath. In reality, the breath is the physical dimension of the emotion, and the emotion is the mental dimension of the breath. Working on either affects the other.