Editing Checklist: Spelling
__ Spell check has been run.
__ "It's" and "its" have been used correctly ("it's" is a contraction for "it is"; "its" is possessive).
__ All other homonyms -- which spell check would not catch -- have been checked. (For example, you wouldn't want to write: "She peaked through the blinds and saw the peek of Mt. Ampersand.")
Editing Checklist: Grammar
__ Dialogue is punctuated correctly.
__ Any run-ons or fragments are intentional (and even those are rare).
__ Subjects and verbs agree in number, and verb tenses are consistent throughout.
__ Commas have been used correctly.
__ "That" and "which" have been used correctly.
__ There are no unclear or confusing pronoun references.
__ Sentence structure varies in descriptive or expository passages. (Keep your reader interested.)
__ The sentences are concise.
__ Consideration has been given to word choice. (This means you have consulted a thesaurus.)
__ Basic facts have been checked (especially ones that would be embarrassing to get wrong).
For more on the last few points, see "Developing Your Writing Style." If you don't know what some of these things mean, refer to a basic style guide, such as the Chicago Manual of Style or one of Kate Turabian's guides. For an online reference, About.com's guide to grammar & composition offers clear explanations for all of the above items, as well as exercises. There are also plenty of books to choose from. I've taught with English Made Simple and Diana Hacker's Rules for Writers, which has online exercises, in the past, but your local library or bookstore (or college bookstore) should have a section of grammar books. Look for one with exercises and a key at the back.
I know many writers feel that grammar isn't important, that it even in some way inhibits their creativity. But you won't hear baseball players admitting that they don't understand the rules of the game. Even artists study things like perspective and the color spectrum. These are our most basic tools. It's worthwhile to get them straight. And in writing -- unlike baseball or painting -- you'll have plenty of opportunities in both your personal and your professional life to make use of these skills.