Ignore them. This may seem harsh, but one of the key ways of responding to your child’s tantrum is to not engage it. …
Walk away. …
Give them what they want on your terms. …
Distract and divert their attention. …
Use humor…
Stay calm….
Think like your toddler. …
Help your child explore. …
But set limits.
Help them give words to feelings…
Teach them deep breathing…
Give plenty of hugs !

Accept that you can’t control it. Do t try to calm the, down, just be there and maybe hold him/her, or otherwise walk away and just wait for it to end.

I think it helps to remember,as you say, it is a stage when their emotions are developing. Often frustration is at the root of episodes. They are not able to communicate what they want; or can’t reach/do something; or just want something that they aren’t being allowed to have and can’t understand why. They scream and yell (and are probably quite scared themselves of the noise they make!). Keeping your cool is important in helping them through it. And not shouting at them but not giving in either. Wait for the yelling to subside and calm / comfort them when it becomes possible so they feel secure after their possibly scary outburst. But make sure that there is no actual pay-off for them for having had a tantrum – like getting the prohibited toy/sweetie. When it happens in public I think it is especially important to keep cool and not care what anyone thinks. SO what if they are yelling and people are watching. Just let it happen and ride it out. Sometimes you can distract/divert attention with a toy/something that just takes their focus away, but sometimes letting them scream is all you can do, making sure they aren’t near anything that can hurt them etc.