Once you have completed your first draft, you should read it through carefully and edit for structure, clarity, and tone. To ensure that these three aspects are adequately covered may well require more than one re-reading and revision.
The first aspect you should check is the overall structure of the piece. Now that you have all the points down in writing, are they in exactly the right order to give the greatest possible weight to your argument? Is the principle of organization clear? Are there any repetitions or digressions you could remove entirely? Are the examples you give clear and relevant to your thesis? As a rule, the strongest point and the best example should appear last, to avoid an anticlimactic argument.
Clarity obviously includes grammar and spelling. However, even a piece of writing that is correctly spelled and grammatically immaculate may be difficult to understand. Look at your draft as a reader, and try to imagine that you are encountering the argument for the first time. Are there any sentences that need to be read twice, or in which the meaning is ambiguous? Are there places where excess verbiage obscures the message? Amend these sentences by breaking them up if they are too long, so that the meaning cannot be misconstrued.
Finally, ensure the tone and vocabulary of the piece are appropriate. Does the draft contain clichés, slang or jargon? Is there excessive use of the passive voice? Are you certain that you understand the meanings of all the words you have used, and does each sentence convey exactly what you want to say? You should also consider any special requirements of your intended audience. This includes any instructions you were given if the draft in question is an assignment. It is always worth checking back to ensure that you have complied with the rubric or guidelines of the assignment.