I focus on giving my kids the vocabulary to express their feelings. We role-play together and I'll ask them to act out hypothetical scenarios, especially emotional ones. For example, I'll say, "You're playing with a friend and a big kid takes the toy they are sharing. How does that make you feel?"
We practice, in a light and playful way, putting words like 'angry', 'frustrated', or 'sad' to these situations. I want them to understand their emotions so that when real-life scenarios arise, they have the language ready.
I also give them simple strategies to calm down when they feel those big emotions. We talk about deep breathing and I'll have them practice it right there: take a deep breath, hold it, and blow out slowly - it helps them pause and regain composure. Or, if they are feeling upset, we talk about distractions; looking at something else, counting backwards, or focusing on something fun to quickly shift their attention.
It's amazing how aware kids become when you give them the language for feelings. They start to notice emotions in themselves and others more and it helps them express themselves clearly. It's a work in progress but I believe these simple techniques are an effective way to begin teaching emotional intelligence.