1. Use as few words as possible; this does not mean short. It means muscular. No flab. Really good writing has an abundance of significant, necessary, and relevant details that will conflict with brevity for the sake of brevity.
2. Many websites can show you how to achieve muscular prose. Some of these techniques should be immediate alarms as you write. For instance, I started this point with "There are many websites that . . ." and I revised before I put the period. "There are" and "there is" openings are usually revisable, as are "It is" openings.
3. Put the most important ideas in the beginning and end of the sentence rather than the middle, and put the important ideas in the independent clause rather than the dependent clause. If you don't know what these terms mean, you have no business writing. While a good writer does not need a Ph.D. in Linguistics, or even a Bachelor's degree necessarily, a good writer must study the English language. A writer cannot simply write "by ear" like a dilettante pianist.
4. English profs will tell you not to use "I." That is generally a good rule. All rules have exceptions. Use the rule when stating an opinion, but state the opinion as an opinion, not a fact. "To be" verbs have the authority of fact when they often are applied to opinions.
5. The past tense can usually replace the past progressive. "She was writing" vs. "she wrote." The first is only necessary is describing a specific action in a specific time frame, rarely for action over time.
6. The pronoun "you" should be used sparingly in most prose. Only use it when what is being written is directly true regarding or attainable by the reader.
7. Spell and grammar checkers are not always right. They will tell you not to use the passive voice, pretty much ever. There are legitimate reasons for using the passive voice; you just need to be perceptive about it. Most of the time, however, the active voice is better.
8. Fiction writing has its own special set of rules.
"He said" and "she said" tags should only be used to clarify who is speaking. They rarely need more than the simplicity of "he said." They get in the way of reading. "He voiced his opinion" for example, is a foolish tag. It should be clear from what he says in the quotation marks that it's an opinion. "He said angrily" is foolish, too. The context and words in the quotation should make it clear he's speaking angrily. Adverbs, then, on the tags should be minimal.
Actions rarely can take place simultaneously rather than consecutively. "He opened the door as he answered the phone" is really hard to do, yet one will often see this kind of thing in fiction.
Adverbs are weaker than verbs. "He said loudly" should be "He screamed, barked, called, yelled" etc.
"To be" verbs are weaker than action verbs. Her dress was beautiful. She wore a dress of ....
Show, don't tell. If having to tell, work hard to make it action-oriented.
You need beta readers. We all think our writing is better than it is.
Watch multiple pronouns of the same gender. If two women are in a scene, it must be clear who is doing what; you can't have "she" or "her" refer to two women at the same time.
Point of view is everything. Ask your beta readers to look at that particularly. A character can only know what he or she can know; no believable character is clairvoyant and can see into another's head. This is the key problem with first person narration.
9. For all writing, return to the basics. Everyone should read Strunk and White periodically. E.B. White knew what he was talking about; he wrote the remarkable Charlotte's Web, for goodness' sake.