For editing, you need to read the paper through and make sure everything is in logical order. (You may end up moving sentences and/or paragraphs around as a result.) Then read it again and make sure every sentence logically follows the one before it in each paragraph.
Here are suggestions for proofreading, which is the next step in getting a paper ready to submit.
Thanks to PsyDAG for the following:
In the future, if nobody is available to proofread your work, you can do this yourself. After writing your material, put it aside for a day — at least several hours. (This breaks mental sets you might have that keep you from noticing problems.) Then read it aloud as if you were reading someone else's work. (Reading aloud slows down your reading, so you are less likely to skip over problems.)
[You can also either read it aloud to someone else or have someone else read it aloud to you! (The latter works really well!)]
If your reading goes smoothly, that is fine. However, wherever you "stumble" in your reading, other people are likely to have a problem in reading your material. Those "stumbles" indicate areas that need revising.
Once you have made your revisions, repeat the process above. Good papers often require many drafts.
And here are three really good websites that will help, too.
You're welcome! =)