A.B.
Ignore the screaming, but don't ignore him. If all you do is focus on his screaming, you will both be frustrated. Ask him quietly what he needs. If he can't talk, but you know what he wants... ask him... ex: Say his name, quietly... get his attention. If he is still screaming, use the words he is looking for. Do you need your sippy cup?
I think he will respond really well if you can speak for him.... use the words he is looking for. Model the right way to talk and show him that he will get his needs met only if he talks like you do.
So don't give him what he needs when he is screaming. Have a conversation with him about what he needs quietly and physically at his level. If he only gets his needs met once he quiets down, he will eventually take the shortest route to getting what he wants and stop the screaming.
I do this with my 22 month old and she always calms down....