Validate, validate, validate.
Children feel many emotions, just like adults. But for some children, talking about their emotions is a bit like nailing jello to the wall. They don't have the language or the experience of feeling the emotion thousands of times to know that it even is a feeling as opposed to something that has taken over them. Try to reach back to when you were a child (try younger than 8ish) and remember when something went wrong, a friend hurt your feelings or an embarrassing moment happened in school. The feeling likely took up residence throughout your body, tears were shed, sobs were heard and your body may have literally collapsed to the floor. It may have felt like the world as you knew it had dramatically shifted. Hopefully, you had an adult nearby to comfort you, talk you through the distress and recount what had (actually) happened. Slowly, you may have started to feel better and get back into the groove of the next activity. As we get older, we learn through experience and being taught, that emotions come and go. They become more or less abstract and for the most part (with exceptions certainly such as grief, major depression, significant anxiety) do not disrupt our world as we know it.
One of the best ways to teach children about the emotions they are feeling is to validate them. This means, bring awareness to what they are feeling - label it! As parents, we often want to "make it better" or have children "not get so upset." But, like it or not, they do get so upset and it isn't better. Try starting with, "You are feeling _______ and it's OK to feel ________." Even when that feeling is sad, jealous, worried or embarrassed. We also must acknowledge what is hard in us about having our children experience those feelings. Why don't we want our children to feel embarrassed? Why are we worried when our children are worried? It is likely driven by a fear that if they are worried, something else may happen - they'll cope with the worry in some way that is harmful, they'll be so worried they won't try new things or they will start to believe that because feeling sad is OK, they will feel it all the time. Then, who is sad? Certainly children and adolescents experience big emotions that do lead to difficult circumstances for parents and families and it is important to pay attention to those, minimizing impairment and distress. Often big help is needed and relieving. But in the meantime, reflect on your own experience and help your child reflect on theirs.