Complete a first draft of the piece you want to write. Before you begin, have clearly in mind the topic, the goal of the writing, and the style in which it should be written, but focus on getting the words down on paper quickly without worrying about spelling, punctuation, or word count.
Spell-check your writing. Go through the manuscript looking for basic errors you can fix. Typos and grammatical errors distract a reader and undermine your credibility as a writer.
Split up long sentences wherever possible. Short sentences are more effective in getting a series of thoughts or ideas across. They keep the reader from getting bogged down in long threads of text.
Split up lengthy paragraphs. Readers lose interest when confronted with long, unbroken columns of type. Short paragraphs make the progression of ideas easier to follow and allow the reader brief moments to digest information.
Trim excess language. Are you using words like quite, rather, and very to help out a weak modifier rather than looking for a more precise and effective one?
Change passive voice to active voice wherever possible. Instead of saying, "The window was broken by Jane," directly state who broke the window: "Jane broke the window."
Print your writing out and read it out aloud with a pen in hand. You will find this makes it easier to spot errors and places where the writing could be more clear and concise.