Imagine mindfulness as a three-legged stool. The seat is mindfulness, the three legs are awareness, acceptance, and compassion (starting with self-compassion). Each leg is one part of a three-step process, to be used in conjunction with awareness of your breathing.
First, present awareness involves focusing your attention on the present place, the present moment--paying attention to where you are right here, right now. By paying attention to what is happening within you and around you, you can calm your mind rather than being "hijacked," without realizing or choosing it, into peripheral thoughts, feelings or things going on in the environment
Second, acceptance. Acceptance does not mean resignation or being passive. It simply means seeing what is happening within you or around you as it actually is in the present moment. Seeing it and stepping back from it, without judging it. By doing so, you are further calming yourself, and allowing yourself to make choices about how you wish to act, or not act, in that very moment. Even if you cannot change an internal or external event, by practicing mindfulness, you can learn to remain calm in the face of it.
Third, compassion, which begins with self-compassion. Self-compassion involves showing yourself kindness and understanding, not judging yourself. It can be very powerful in creating a sense of calm and joy. As you show compassion towards yourself, you are better able, and more willing, to extend compassion to others.