Here are the foundations of self calming, per my work with anxiety, panic and post trauma patients.
Anxiety feels like a response to external stressors, with the implied inaccurate belief that one can only relieve anxiety by solving the conflict. Brains have a subconscious alarm system, the amygdala. It tells the body when to release adrenaline into the blood stream. Adrenaline response evolved to help escape existential threats, fight or flight. It doesn't differentiate between falling off a cliff and interpersonal conflicts. Muscle tension, rapid, shallow breathing, eye dilation and circulatory disturbances, while useful in fighting or fleeing, are problematic in most modern stressors, including relational conflict. Learning to monitor one's adrenaline/arousal and deliberately reduce it when unneeded is tremendously useful.
Adrenaline breathing, rapid and shallow, does not purge CO2 fully from lungs, and reduces intake of O2. Feeling difficulty breathing stimulates the adrenaline feedback loop, so brain releases more adrenaline. This is the etiology of panic attacks, basically adrenaline storms.
Slow, deep breathing with complete emptying of lungs while exhaling is a strong antidote to adrenaline overload. There are many online resources to guide this process. It takes regular practice to become fully effective. Practicing calming breathing for 2 min. intervals, 10-15 times per day over 2 weeks will teach your brain and body to turn down the adrenaline valve. This practice works best when relatively calm, to focus on the internal process. Once learned, this breathing will be effective quickly against excess adrenaline. Using breathing as a relief only when anxious is far less effective than practicing/learning over time to be well armed when major stress/anxiety takes over. One reason exercise is effective for stress is it facilitates full breathing.
Another basic self-calming skill is grounding, I'll post on that later.