When my friend with 2 daughters did this I just about died and thought her the worst mother in the world. Then when my son started pulling this stuff, I figured out why she did this and started doing it to. Now, this only works with typically developing children-children with sensory issues, add/adhd/autism/aspergers or whatever are not going to get this message the way we need them to, so if your child falls into one of those catagories, talk with your therapists about what works best.
When precious starts throwing a fit, calmly tell your loving child that you cannot understand him when he is screaming and carrying on, that you know he wants to talk with you, and when he can, to come get you. Then walk away and ignore him and the behavior (as long as he is not throwing and breaking stuff, coming at you with a knife etc!). Do this everywhere it is safe, the grocery store (if you are in a safe one where you know the staff and they won't call child protective services on you!) everywhere. I explained in advance to my son that when he gets upset and doesn't talk with me I can't understand him when he is screaming. If he gets upset and cannot talk with me, he needs some alone time and when he is ready to talk with me and listen to me I am all his...otherwise, I will walk away so he can have some alone time. So, first time he pitched a fit after that talk was in a grocery store, and so I walked away, and walked away and walked away as he followed me having his fit. He finally got the message, stopped the fit, and told me what he wanted and accepted when he was told he couldn't have what he wanted. This was not foolproof, but it worked alot until he got his skills in speech and self control up and working. Now, we also told him that if he needed to pitch a fit or make ugly noises or faces etc, he could do that in the bathroom (that way if this behavior started in the grocerystore, he would have somewhere to go to get it out of his system and get control again. Telling him he can do it in the bedroom doesn't work when you are at school, a movie, or the store!). This gave him an alternative, and a face saving method of regaining control. When told he had a choice of going to the bathroom to get this out of his system or behaving and talking so I could understand him, he usually chose the latter. Good luck!