I believe the road to hell is paved with adverbs, and I will shout it from the rooftops. To put it another way, they're like dandelions. If you have one on your lawn, it looks pretty and unique. If you fail to root it out, however, you find five the next day… fifty the day after that… and then, my brothers and sisters, your lawn is totally, completely, and profligately covered with dandelions. By then you see them for the weeds they really are, but by then it's—GASP!!—too late.
King sets up the strawman of the evil adverb by providing numerous examples of appalling misuse, with which he then attempts to tar an entire part of speech. American authors, who were never completely comfortable with the adverb, often misquote King as saying one must never use adverbs. That is obvious nonsense. British authors (and by extension, Canadian writers) being native speakers of English are better equipped to use the adverb correctly. Far worse, in my view, is the inexcusable American habit of dropping the 'ly' from an adverb and pretending it is an adjective. But King is correct about the overuse of adverbs, if one is not cautious about their proliferation.
As with said bookism, adverbs in dialog tags must be used sparingly. As discussed in Common Errors episode 13, we usually don't need to spell out how something is said. If the dialog is well written, it is usually self-explanatory:
"I hate you!" Frank said angrily.
We knew that Frank said that angrily from the words and the exclamation mark. The adverb sticking out can sometimes tip you that the entire tag can be deleted.
By extension, some caution is required not to overload adverbs onto self-explanatory actions:
He angrily threw down the gauntlet.
Do we really need "angrily" in there? I think not.
Having "angrily" included creates three problems: First, its redundant, so removing "angrily" tightens the text, which I've suggested earlier means faster pacing, more tension, better action. Second, it restricts the reader to a single interpretation of "threw down the gauntlet" and in the reader-director's cut, that might have been better rendered as "haughtily" or "carelessly" or whatever. Don't try to overcontrol the script. Third, "angrily" is an example of that most basic of errors, "telling, not showing". If you have to tell us the character is angry, then you're probably not doing it right. We need to see anger in their body language, in their actions (throwing down a gauntlet, for example), in their choice of words, the punctuation, and so on. Too many adverbs may be a sign that the author is giving the reader the outline rather than the story.
A few deftly chosen adverbs can refine descriptions, occasional use in dialog tags and action scenes can provide necessary stage directions, but each use of an adverb should be interrogated to ensure that it's necessary.