[The] tendency to describe a character's emotion may reflect a lack of confidence on the part of the writer. And more often than not, writers tell their readers things already shown by dialogue and action. It's as if they're repeating themselves to make sure their readers get the point. So when you come across an explanation of a character's emotion, simply cut the explanation. If the emotion is still shown, then the explanation wasn't needed. If the emotion isn't shown, rewrite the passage so that it is." (Self-Editing for Fiction Writers, p17)

As a general rule, if you feel you need an adverb, you have failed to convey an emotion or character trait through your dialogue and action.  If everything else is working, you can delete the adverb with no negative impact on the story. As the tip says, the tendency to over-describe is most prevalent when describing emotion, but it carries over to all descriptive elements.

Here are some examples from my own writing. In each case, deleting the "-ly" word strengthens the sentence. It also gives me a chance to evaluate the sentence and make sure that either the sentence itself, or the story around it,  has the necessary elements to convey the impact of the removed word.

Keri knew Robert was seriously beginning to doubt her abilities.

What I meant to imply here was that Keri had a track record of failures and was one step away from being fired. Robert was serious in his disapproval of her work, and the situation was dire, but none of that is conveyed by the "seriously" above.

She stared at him silently, willing him to go away, then bent back to her work.

In this snippet, the character was annoyed with the "him" and was giving him the silent treatment in the hope that he would stop pestering her. All this was expressed in the previous sentences, and as she's not saying anything here, the "silently" is redundant.

Heather blushed lightly and looked down at the table.

Blushing lightly is a subjective and weak description. Something like "Heather's cheeks flushed pink and she looked down at the table." can be more effective. This gives the reader a concrete detail to latch onto and makes the scene more immediate.

And, my most blatant example:

"Travis! My office. Now.” Professor M said loudly from the lab doorway.

The exclamation point is more than enough to convey volume, don't you think? These are the kinds of mistakes that are easy to make while writing, but just as easy to clean up when you begin editing. An overabundance of adverbs is the mark of a novice writer. There are many ways to flush out weak or overblown description, but searching for "-ly"s is the fastest way to tighten up your writing.