For children to develop better emotion regulation, it can help them to think about the 'gap' between the trigger that caused them to feel any particular emotion and their behavioural response. In other words, consider what happens in that gap and what they can do or think so that their response is more productive or at least less damaging.
For younger children, it can be as simple as getting them to focus on where inside their body they are feeling the emotion, taking some deep breaths, repeating the mantra, 'I have a choice about what I do next,' or getting them to name their emotion - so that there is a gap between trigger and response. Once the intensity of the moment has subsided, they are far more likely to be able to engage their thinking brain and consider the choices available to them rather than simply having a knee-jerk reaction.
For older children, it can be helpful to look a bit further into the process of emotional reaction as follows. There are two stages between the trigger and the response (interpretation and arousal - see below) and for every individual these stages will be unique to them based on their values, their temperament and past 'wounds'.
You can ask older children to consider the 'interpretation' part of this process and help them to engage in 'reframing' what happened so that their emotional response is not triggered so strongly. Reframing generally requires a person to shift their focus from themselves and wonder what is going on for the person causing the affront. Simple thoughts like,
she must be having a really bad day
he must be tired and grumpy
perhaps she is cross with me about what happened earlier
he must be worried about something
can make your child a little more forgiving about potential triggers. That is not to say your child has not got the right to explain how they felt when the other person behaved the way they did but it makes an escalation less likely and some shared understanding far more likely to be achieved.