I think I've posted some of this on other threads, but here goes.
1. Tell him he has the right to have his emotions & feelings but he does not have the right to make the rest of the household miserable with them. Sometimes alone time is useful (for him, or for you).
2. Teach him about how emotions can be experienced as waves, and that when he is feeling them intensely he can try and "surf" them - not let them tumble him around
3. Try to help him to articulate his feelings - angry, sad, scared, worried, irritated anxious, excited, thrilled, full of joy, content, calm. Even as an adult in my 40s, I sometimes experience excitement or anticipation as anxiety & then only realize when I am doing the thing that I thought I was anxious about, I'm having a great time and that it was being "pumped up" that I had been feeling, not anxious.
4. Sometimes w/ some people "least said, soonest mended". If he seems a bit out-of-sorts, well, let it lie a bit and instead offer pleasant action.
Example, my kids LOVE mashed potatoes - so if my son seems a bit down when after school (when I've come home from work), I might ask him to peel the potatoes for mashed, or make the mashed potatoes & that action helps him forget whatever he's brooding about & also helps give him a happier frame of mind.
5. Try to help him put things in perspective. If he's upset about a teeny tiny issue that he was upset about before & it worked out OK; remind him of that. If you both have humor that bends in that direction - introduce the "First World Problems" meme.
6. Some people theorize that "venting" can help - but sometimes it can instead kind of get into a feedback loop; so instead, try to help him learn to keep his voice down & calm when expressing his feelings.
People often need time to process things or make transitions. Try to make room in the household schedule for that. If he gets emotional about sorting through his school bag when he gets home - let him come home & cool out for a while before moving him on, maybe a 30 minute "rest break" on arrival before there are other things to do.
Just hanging out together sometimes is good; other times a "Hey, you seem tired/down/ do you want a hug/hot bath/etc." and if yes - give it and then leave off; if no then say a cheerful "OK" and then don't try and dig into it deeper. Kids also sometimes need emotional space.
Acknowledge sorrow or problems "Wow, that's too bad...want to tell me more" but resist the temptation to try and fix it, at least immediately.