There are many different ways to watch the breath. In the Zen tradition we may be asked to simply count the breaths. Begin with the inhalation that is one. The exhalation is two. The next inhalation is three. Keep counting until you reach ten, and then begin over at one with the next inhalation. If this becomes easy, and you can count to ten without getting lost, without reaching twenty, or without counting mechanically in the background, then try to count only the exhalations.
This approach is sometimes called “shamatha” with support. Shamatha is one permissible way to meditate in all schools of Buddhism and other spiritual paths, as well as in the yogic schools.  Shamatha means calm abiding, tranquility, or meditation – as we sit and breathe, we just sit and breathe. Nothing special is happening, nothing special will ever happen that is what makes this practice so special.
In the vipassana tradition you may be asked to follow the sensation of the breath – notice how it feels to breathe in and out. Where do you feel it? You may be asked to follow the feeling of the air on your upper lips as you breathe, or to follow the feeling in the throat, belly, or chest.
Please note: we are not trying to change the breath in any way. Our approach is very yin-like: we accept the breath the way it is. In very active yang styles of yoga, we do try to change the breath – for example, when we perform ujjayi breathing. In pranayama, we very obviously try to change the breath. But, in shamatha or vipassana, we want the breath to be whatever it wants to be: we accept it as it is. This is not easy! As soon as the mind tunes into the breath, it tries to control it, perfect it. Drop the effort and just watch. Watch the beginning of the inhalation, notice the exact moment the inhalation ends, the moment the exhalation begins, and the exact moment the exhalation ends. Notice the slight pauses, if any, between the in and out breath, and the out and in breath. Don’t try to create, force, or do anything.
Of course, you need not only follow the breath while meditating in a sitting posture; you can do this while walking as well. In Zen this is called “kinhin.” Walk slowly or quickly. Walk indoors or out in nature. However you choose to walk, watch the breath. Every time you notice your awareness has wandered away, simply bring it back to this breath.