Below are two rules from Strunk and White's classic writing guide.
From the chapter An Approach to Style:
16. Be clear.
Clarity is not the prize in writing, nor is it always the principal mark of a good style. There are occasions when obscurity serves a literary yearning, if not a literary purpose, and there are writers whose mien is more overcast than clear. But since writing is communication, clarity can only be a virtue. And although there is no substitute for merit in writing, clarity comes closest to being one. Even to a writer who is being intentionally obscure or wild of tongue we can say, "Be obscure clearly! Be wild of tongue in a way we can understand!" Even to writers of market letters, telling us (but not telling us) which securities are promising, we can say, "Be cagey plainly! Be elliptical in a straightforward fashion!"
Clarity, clarity, clarity. When you become hopelessly mired in a sentence, it is best to start fresh; do not try to fight your way through against the terrible odds of syntax. Usually what is wrong is that the construction has become too involved at some point; the sentence needs to be broken apart and replaced by two or more shorter sentences.
Muddiness is not merely a disturber of prose, it is also a destroyer of life, of hope: death on the highway caused by a misplaced phrase in a well-intentioned letter, anguish of a traveler expecting to be met at a railroad station and not being met because of a slipshod telegram. Think of the tragedies that are rooted in ambiguity, and be clear! When you say something, make sure you have said it. The chances of your having said it are only fair.
From the chapter Elementary Principles of Composition:
17. Omit needless words.
Vigorous writing is concise. A sentence should contain no unnecessary words, a paragraph no unnecessary sentences, for the same reason that a drawing should have no unnecessary lines and a machine no unnecessary parts. This requires not that the writer make all sentences short, or avoid all detail and treat subjects only in outline, but that every word tell.
Many expressions in common use violate this principle.
the question as to whether / whether (the question whether)
there is no doubt but that / no doubt (doubtless)
used for fuel purposes / used for fuel
he is a man who / he
in a hasty manner / hastily
this is a subject that / this subject
Her story is a strange one. / Her story is strange.
the reason why is that / because
The fact that is an especially debilitating expression. It should be revised out of every sentence in which it occurs.
owing to the fact that / since (because)
in spite of the fact that / though (although)
call your attention to the fact that / remind you (notify you)
I was unaware of the fact that / I was unaware that (did not know)
the fact that he had not succeeded / his failure
the fact that I had arrived / my arrival
See also the words case, character, nature in Chapter IV. Who is, which was and the like are often superfluous.
His cousin, who is a member of the same firm / His cousin, a member of the same firm
Trafalgar, which was Nelson's last battle / Trafalgar, Nelson's last battle
As the active voice is more concise than the passive, and a positive statement more concise than a negative one, many of the examples given under Rules 14 and 15 illustrate this rule as well.
A common way to fall into wordiness is to present a single complex idea, step by step, in a series of sentences that might to advantage be combined into one.
Macbeth was very ambitious. This led him to wish to become king of Scotland. The witches told him that this wish of his would come true. The king of Scotland at this time was Duncan. Encouraged by his wife, Macbeth murdered Duncan. He was thus enabled to succeed Duncan as king. (51 words)
Encouraged by his wife, Macbeth achieved his ambition and realized the prediction of the witches by murdering Duncan and becoming king of Scotland in his place. (26 words)