How do teachers teach emotional regulation in a classroom setting?

I think this is along the lines of the "feeling thermometer", but last year my kindergartener used the Zones of Regulation a lot. His teacher introduced this method to them and they used it quite a bit throughout the course of the day. It was a sheet that had four zones (red, yellow, blue, green) and described each zone. The kids then had cards with each color. So, when the teacher asked them how they felt, they didn't even need to speak - they could just show her the color of the card.

Now, as a first-grader, he told me they no longer do it, but I did speak to some other children the other day who were actively referencing the colors and I thought it was wonderful. We try really hard to use the same colors and this simple method at home.

Our behaviors are driven by our emotions. Children who fail to regulate their emotions, find it hard to focus on their learning.
I strongly believe that good teachers not only help their children in accessing new knowledge, they also support their children in learning adaptive behaviors and skills so they can excel in their lives.
As someone who has been working with teachers very closely, I think there are few strategy that work quite well for children of all ages. If you keep reorganizing your classrooms on regular basis, children get to sit and interact with different children. It provides them with flexibility and empathy to interact and cooperate with different types of personalities.
Teaching children the relaxation techniques such as deep breathing and muscles relaxation (stretching and relaxing different muscles) also helps them in regulating their own emotions. Teachers sometimes make deep breathing a part of their class routine. Having a one minute deep breathing and muscle relaxation break once or twice in the class can be very effective in reducing emotional outbursts in the class.
I have noticed that keeping students mentally busy helps them in focusing more on positive activities. Having learning stations which provide activities at different difficulty level and with different learning preferences also help in engaging diverse emotional and learning needs of learners.
At times teachers also allow few students to use fidget spinners, bands and other such toys for having a better control of their emotions.
Teacher has to become a positive role model for the students. With constant support, children gradually learn to regulate their behaviors.

As someone who regularly works with kindergarteners and first graders, I have had many conversations with teachers about the importance of helping kids to recognise and regulate their emotions, and also to normalise the fact that we all feel these emotions. Many teachers recognise the value of including a "calm corner" into classroom spaces. The purpose of this space is to provide kids who are feeling overwhelmed or dysregulated somewhere safe away from the primary learning space to spend a few minutes. It should only be used as a positive space for a necessary "time-out", and never as a form of punishment. In creating a "calm corner", the goal should be to ensure that the space is soothing and can assist the child as they work to regulate their emotions.

Another good classroom tool is a "feeling thermometer" for each child. This can take the form of a poster showing pictures of various emotions and kids can use a marker to identify how they are feeling. When the teacher is aware of any concerning emotions, they can find opportunities to discuss how these feelings make you feel and what can be done when you feel this way. As teachers normalise discussions about feelings, children will become more comfortable talking about their emotions.