See, to me a question like that should be about literary style--you know, does the person use long sentences or short ones, is their writing lyrical, that sort of thing. But if you are proofreading, style means, essentially, correct grammar, punctuation, and the like. A professional proofreader reads for style as well as spelling and typos--which doesn't mean that if your writing sucks, they'll make it better (unless it's obviously awkward or incomprehensible, in which case they'll suggest improvements).
Why people who write books on grammar like to call it style, I do not know. I assume it's because language is a human creation, so when we talk about rules of grammar, we're just talking about rules that people have agreed on. Different people prefer different rules. So, the English put commas everywhere--that is their style--and Americans don't. But it's not like there's some law of physics out there preventing you from using no commas or nothing but commas--you can if you like (just don't get all whiny when no one understands what the hell it is you're trying to say).
In the publishing biz, there are two dominant style guides: The Chicago Manual of Style and The AP Stylebook. Chicago style is used by book publishers, while AP style is used by newspapers and magazines. Actually, to be precise, Chicago preferred style is used by book publishers.
What am I talking about? Well, let me describe The Chicago Manual of Style: It is roughly the size a dictionary. It is a reference book designed for professional proofreaders--it is supposed to be on your desk at all times, and you are to look things up in it to see if they are correct.
Once you do, Chicago is going to give you the entire story surrounding your grammar conundrum. Wanna know if it's "Douglas' dog" or "Douglas's dog"?* Chicago will give you no fewer than three different version of the rules to chose among: One version says that "Douglas'" is correct, and two versions say "Douglas's" is correct. One of these rules ("Douglas's," unless he is actually Jesus or Moses) is their preferred rule.
So, really, you can use Chicago one of two ways: You can follow Chicago preferred style, or you can rely on Chicago to tell you the outer limits of what is acceptable ("Douglas's dog" or "Douglas' dog" but NOT "Douglas' came over for dinner," or God forbid, "Douglas's came over for dinner"). If you have some stylistic quirks that you are really attached to, take a look in Chicago--chances are that if it's even remotely acceptable somewhere, it's in there, and then you're covered.
The main problem I find with Chicago is that even Chicago preferred style is full of weird little exception (like "Jesus'" and "Moses'"), and as a result, it is hard to memorize. This is NOT true of The AP Stylebook. AP was written for reporters who cover breaking news. They can't carry around a damned dictionary, and they don't have time to look up some damned rule--they have a deadline to meet. NOW. Wondering about Douglas and his dog? It's "Douglas' dog," period. End of story. On to the next rule.
A lot of writerly types whine about AP style because they feel like it's less literate, less traditional, less booky, less beautiful, less individual, less whatever. But it's easy to learn, which is no small thing if you are trying to produce clean copy. When I worked in publishing, the only people who really knew Chicago preferred style were the copy editors. In contrast, I would say that just about everyone who works in journalism in any sort of writing capacity carries AP style around in their head--I certainly do.
Obviously, you can have your own preferences (I do--look at that footnote down by the asterisk), and if you are writing speculative fiction, or fiction about children, or fiction set in a community that uses non-standard grammar, you may have to make up your own rules, just as you may have to make up words. There's also a lot of drama to be had by deliberately breaking the rules (for example, when a character is breaking down under stress). But if you give the impression that you never had any idea what the rules were to begin with, that's a problem: You may think that you're so very brilliant that you don't have to follow the rules, but you shouldn't expect the same indulgence from readers.
* Bonus points if you noticed my random use of British style here! I like to put punctuation outside the quotation marks when it's not actually part of the quotation, which is not the traditional American way. I was kind of sneakily doing it before I read Eats, Shoots & Leaves (which is a very entertaining book on grammar by a Brit) and was thoroughly convinced that the British way really does make a lot more sense. Now I'm trying to set a trend....