Set your paper aside for at least 24 hours before editing. This will give you just enough space from your work that you can read it with a clear head.
Run spell and grammar checks on your paper through your word processor.
Read your paper through once, making note of any spelling or grammatical errors your word processor may have missed. Be sure that you do not rely on your word processor to catch every error for you -- it is not foolproof.
Check the style of the paper. Make sure that your paper is written in the specified format (typically AP or MLA) and that your have correctly cited your sources. If your paper is supposed to be informative, make sure it does its job of providing readers with facts. Likewise, if it is supposed to be persuasive, ensure it persuades the reader to consider the point-of-view offered in the paper.
Check presentation. Make sure you have properly indented and spaced your paper, including your title and works cited pages.
Read through your paper once more -- out loud. Hearing the flow of your sentences spoken aloud will bring any grammatical mistakes to your attention that you may have previously missed.