What should a mother do if her child won't stop screaming because she doesn't buy him some toys in the store?

Seriously.  These kind of tantrums usually feed on either exhaustion/ hunger or parent's fear of public embarrassment.  If it's the first, you need to get out, the kid is done.  Either buy the minimal amount that you already have (with screaming kid), or drop everything and walk out.  If it's the second, the kid is banking on you being too embarrassed to do anything but cave - it's just going to continue or worsen the longer you're in there.  Either buy the minimal amount you have (with the screaming kid), or drop everything and walk out.Stay calm, when you get to the car, figure out which it is (if the tantrum is over, was likely the first, you can find out quickly enough if it's the other two).  Just stay in control, don't get angry.  Remember, kids have very little control, few communication tools, and almost no coping skills.  Anything they get, they get from you.  They aren't trying to piss you off (most of the time) - they're just trying to make their world work better for them in one of the few ways they know how.

She should try to divert her child attention towards more feasible thing.