I think there's a great temptation to explain too many things to our readers, most likely because in the first draft we are still trying to explain them to ourselves. :)
It's taking me quite a while to do, but I am going through sentence-by-sentence and editing out every unnecessary word.
I've found one of the biggest problem areas I have is my dialogue beats.
I probably have a million -ly endings tagged on to words, for a quick adverb fix.
He said sincerely. She laughed awkwardly. He grinned widely. She inhaled deeply.
Now, I think you can get away with the occasional -ly ending, but not when you are using it as a cop out instead of coming up with clever, specific language.
Instead of telling the reader how something is said, find a way to show that. How did the character's facial expression change when he or she heard the news? What can the character be doing in the background of a conversation that will mirror what is happening in the literal conversation?
Try doing a Google Images search for facial expressions you imagine your characters to have. Or, grab a mirror and imitate the expression with your own face. You may be surprised what you come up with.
If you're like me, you might have a lot of inhaling, coughing, and giggling. Be on the lookout for pet words you use frequently. It's okay to repeat yourself, but not to be redundant.
If you get rid of these -ly endings, you may have more words, but your sentence will likely be less wordy. Big difference.
Also, try this exercise: pick a particular passage in your WIP that you know is wordy. Then, go through and cross out every word that is not furthering your paragraph. This exercise might shrink your paragraph down to a couple sentences, but that's okay, because it will likely help you come up with new material.
Any time you can avoid wordiness, you pack more meaningful information into each word, just like a poem. This helps with pacing. And strong pacing is always a good thing.
Questions for comment: What strategies do you have to avoid wordiness? Are there any particular ways that you struggle with this topic?