In professional publishing, it’s traditional to have editing followed by proofreading – these are two separate processes practiced by specialists in each. In a business, if you’re the only thing between a submitted article and the rest of the world, you’ll have to do both. But it’s still wise to keep them as individual tasks.
Editing comes first. To do this properly, you need to know the audience. If you commissioned the piece, you should have told the author as part of the brief, but if not, you’ll need to get that information from the author. Then read it through without making any corrections; this is important, or you may end up doing unnecessary work such as adding information which actually turns up later.
Now you can get stuck into the editing. That means correcting for style and grammar, reordering content if necessary, and elaborating or simplifying as appropriate. You may also need to do any fact-checking and sort out attribution.
While the end product should be suitable for publishing, it still requires proofreading. Ideally this is done in the published form, so you can check the typography, line breaks and general setting. If your editing was good, there shouldn’t be any spelling or grammar errors at this stage, but in the real world it’s quite possible. To check spelling, someone I once knew would take a copy of a document, replace spaces with line breaks (to give a list of all the words in a document), sort them into alphabetical order, then go down the list looking at each word out of context.
Of course, there are many good computer tools available now to keep on top of grammar and spelling, but they don’t know your style out of the box, and will always have issues with internationalised English, so needless to say, be careful.
Finally, for a document with web links, check them all, and check them again.