How do editors work around any profanity that the author may include in the dialogue?

It would depend upon the nature of the profanity and the way it plays out in the story.  I think you need a specific example to render a guess on what would be done to rewrite or integrate it.

The current, standard method is to use symbols, like this sh#+.

As you are clearly never going to write a book anyway, it hardly matters, does it.

Censorship has changed over the years. 

Editors don't "work around" anything. They point out words or phrases that might be unsuitable or inappropriate for the intended audience, or that might prevent the book from being published. It's then up to the author to change or remove them, or argue for keeping them.

Would the editor "work around it"?  It's the author's right to choose the words, and the author's responsibility to defend his choices or to be careful in choosing his words

The editor can suggest to the author that he use "He swore at me." instead of using the actual swear words. The editor could suggest that the author use fewer profane words and sentences. He could suggest that the author use milder words. (When PM Pierre Trudeau said "Fuddle Duddle" in the House of Commons, it became an instant catchphrase across Canada. Every school kid was calling everyone and everything "fuddle-duddle" and our parents were talking about Mr  Trudeau's language and what he really wanted to say but couldn't because the word was "unparliamentary" and he would have been cut off and censured by the Speaker. Context and audience,  you see, are important. Mr Trudeau could have said, and likely did say, a more controversial word when he closed the door of his office.)

But the author makes the change. Or he doesn't and the editor decides whether his press will publish the book after all.  You don't expect a religious books publisher to print the dirty words, just as you don't expect a publisher with a reputation and sales to protect to print without a lot of thought what could bring about a lawsuit  and a court injunction and a loss of revenue.

Think of the context of your words and think of your readers. You are writing to convince readers that you are the good guy with a grievance, right? The Hero of your autobiography. You want the readers on your side. Choose all your words in your final drafts with care.  If you are pitching your book to rough tough men and women, you write what they want to read, which I think includes "bad language". If you are pitching your message to sweet maiden aunts, you use few, if any, "bad words".

Good editors don't "work around it," they read it in the context of the work and judge whether or not it fits the intended purpose and audience.

The standards applied for a children's book would obviously be very different from one aimed at adults.  Editors will also consider whether the profanity supports or distracts from the overall story.

I recall a book written by an Iraq War veteran, for example, where the editor objected to the fact that just about every line of dialogue included profanity.  The author/veteran assured him that was exactly how soldiers talked in war zones.  The editor said he understood, but since the vast majority of their target audience has never been in a war zone he felt that the prevalent use of profanity would stand out in readers' minds more than the story itself.

Remember, Dan, editors do not change the author's writing choices. Many don't even change authors' mistakes, just note them for the authors to correct, usually with a source for why it's wrong. (Often it's the Chicago Manual of Style or Merriam Webster.) It's not the editor's manuscript to change; it's yours.

Later, in proofreading, goofs that slipped past editors do get corrected. Maybe you typed "in" when you meant "on" or "it." The eye sees what it expects to be there, not what is there, and it takes a skilled proofreader to find and fix those.

If the dialogue (or exposition) has profanity, the highest level editor--the one who's about content--may discuss whether to soften it, depending on the anticipated readership. A book aimed at young teens, for instance, is unlikely to have the F word.

But most of the time, in works written for older teens or adult readers, all those strong-language words and phrases stand as written.

If you are hiring your own editor, they'd better be able to handle the words adults use. If they are uneasy with them, they're not qualified to edit.

It depends on the context and intended audience.

They don't necessarily. If there is reason to, like if they're editing a program for broadcast television where such profanity isn't allowed, they either omit the profanity or substitute the profanity with a euphemism for that profanity, so they may change the F-word to "fudge" or "screw," the S-word to "shucks" or "crap," etc.