meh, I'm still figuring it out. FWIW I've had years pf practice with adults tantruming in my paddy wagon and the same techniques work with them lol.

What worked with DD was me using a low even tone, down at her level and just quietly. I would say "when you're finished let me know" and walk away. Even now she sings out after a couple of seconds "I'm finished mum!"....deal over lets move on to something else.
If she's being dangerous/kicking/arching whatever I pick her up and put her in her room. Not as punisment just because it's safe and her space in there....and I don't have to watch the tantrum which just gets me antsy. I have added "I'm not going to tolerate that behaviour" to the monologue.
While they are so little I didn't find explanation worked for us (and even with fantastic linguistic and understanding skills, only occasionally), just as long as she knew what I expected.

When we're out I use the same monologue and we go to the car if she hasn't stopped on three and go home. Only took a couple of times of ceasing activity before she understood.