An article by Taitaku Pat Phelan explains how we follow our breath when we sit:
The effort we make in zazen is not to hold our minds empty or blank or void of thought. Nor is it to force the attention onto the breath. That would lead to rigidity, to a rigid state of mind.
Rather, our effort should lead to flexibility by being ready to let go whenever we notice that we are distracting ourselves from our intention to engage with our present body and mind. Be ready to let go of distractions, to let go of insights, to let the tracking mind stop and return to your breath.
We do not try to stop our minds from thinking. In zazen, we try to wake up.
When you realize that you are thinking, let go of your thoughts the way you let go of your breath when you exhale. This flexibility, this ability to drop distraction and return to the breath, over and over and over throughout zazen, is one of the most important elements in practicing zazen.
This ability to let go is essential. We can use it to let go of the stickiness of our attachments, to let go of our point of view, to let go of our pain. And whether we like it or not the inevitability of our life is to let go — and we have the opportunity to practice it now.
This effort requires a lot of patience.