It's a delicate business, but it can be done well. Examples from published fiction that you might find of interest below.
I've also included a few examples from my own work -- including a passage where I commit the very sin I've been talking about here.
A lot of the second novel in the Wilderness series takes place in lowland Scotland in 1802. The language spoken by the characters would have been Scots -- not English. I'll spare you the discourse on the difference at the moment, but while I was writing the novel I struggled with representing Scots in writing, and I did end up using spelling, to some degree. Here's an example:
Geordie nodded and cleared his throat. "On the road fra Corbelly, it was, at dusk. A whole pack o' redcoats wi' baig'nets at the ready, marchin' the crew o' the Jackdaw oop the road tae Dumfries. One o' the redcoats was carryin' Granny Stoker on his back, tied han' and fit like a calf. A mair crankit auld chuckie ye'll nivver see, swearin' and skirlin' and screechin'. It was a wonder tae behold."
This is what happens if I change all the spelling to standardized orthography:
Geordie nodded and cleared his throat. "On the road from Corbelly, it was, at dusk. A whole pack of redcoats with bayonets at the ready, marching the crew of the Jackdaw up the road to Dumfries. One of the redcoats was carrying Granny Stoker on his back, tied hand and foot like a calf. A more cranky old chuckie you'll never see, swearing and skirling and screeching. It was a wonder to behold."
All I can say in my own defense is, I tried it both ways and it just didn't read right without the spelling changes. Is the effect such that the characters are trivialized? It's a little hard to tell from this passage, which is supposed to be funny, but I hope that wasn't the case. I worked hard to avoid it. The bottom line is this: I could have ignored the dialect issue and had them all speak the same, but that just didn't work for me; it would have felt like cheating.
The last example is from Curiosity, the character who so many of my readers claim as their favorite. She is an elderly black woman, a freed slave.
"No need to get particular with names, now. Don matter anyway, cause the man who lay claim to Selah wouldn't sell her, and there ain't a law that say a slave owner got to sell a slave at any price if he he got a mind to keep her. So maybe you'll understand that we ain't got much choice, not with a child on the way."
I'd be curious what folks think of the examples below -- which I think are all well done.
Flowers from the Storm, Laura Kinsale
"Bless me, what a row that was, Miss Timms! Shev was right bosky, do you see—he was used up. Corned, pickled and salted—"
"Comatose, Miss Timms," Durham explained gravely. "In strong drink."
"Oh, yes, good Oxford word. Comatose!" The colonel seemed to find that description an uplifting one. "Perfectly senseless. And we was having to carry him home, y'see, between the two of us, and he weighs—'S blood, he must weigh fourteen stone! And who might drive by at the very moment but the one they call the resurrection jarvey—"
"Night coachman. Sells bodies to the surgeons," Durham interpreted. "For anatomy lectures."
"Right! So what should I think—and it was my idea entirely, I promise you, Miss—and the fellow took him, and—" Colonel Fane made an expressive revolution with his forefinger. "And, y'know—his clothes, we got those, and the fellow took him in a sheet to old Brooks! In Blenheim Street! Took him there, to the lecturer's door!" He leaned back his head and thumped the table. "And offered—and offered . . . him for . . . f' . . . sale!"
This passage is especially nice because of the way the Kinsale has used the idioms of the time (early 1800s) in this back-and-forth between friends. It works on a number of different levels. The next passage is from Proulx's
The Shipping News:
They went into the dull gloom of the shop.
"Ah," said Yark. "I 'as a one or two to finish up, y'know," pointing to wooden skeletons and half-planked sides. "Says I might 'elp Nige Fearn wid 'is long-liner this winter. But if I gets out in the woods, you know, and finds the timber, it'll go along. Something by spring, see, by the time the ice goes. If I goes in the woods and finds the right sticks you know, spruce, var. See, you must find good uns, your stem, you wants to bring it down with a bit of a 'ollow to it, sternpost and your knee, and deadwoods a course, and breast'ook. You has to get the right ones. Your timbers, you know. There's some around 'ere steams 'em. I wouldn't set down in a steam timber boat. Weak."
You'll note that Proulx does use some spelling changes to indicate dialect here, particularly the deletion of syllable initial /h/. It's not extreme, and so it doesn't distract -- but she walks a fine line. I think it ends up working because the rhythm of the passage and the use of sentence tags and prefixes:
see, var, you know.
The next example is from one of my all time favorite short stories, "My Man Bovanne," by Tone Cade Bambara . It's written in first person, and the narrator is Hazel, a black woman at philosophical odds with her grown children: she's too old-fashioned for their sensibilities. Bambara was a prominent African American writer who was intensely involved in urban culture in the '60s -- and she writes Hazel's POV in Hazel's language, Bambara's own language, full of imagery and living sound. She could write this vernacular because it was her own.
"Generation gap," spits Elo, like I suggested castor oil and fricassee possum in the milk shakes or somethin. "That's a white concept for a white phenomenon. There's no generation gap among Black people. We are a col—"
"Yeh, well never mind," says Joe Lee. "The point is Mama well, it's pride. You embarrass yourself and us too dancin like that."
"I wasn't shame." Then nobody say nuthin. Them standin there in they pretty clothes with drinks in they hands and gangin up on me, and me in the third-degree chair and nary a olive to my name. Felt just like the police got hold to me.
"First of all," Task say, holdin up his hand and tickin off the offenses, "the dress. Now that dress is too short, Mama, and too low-cut for a woman your age. And Tamu's going to make a speech tonight to kick off the campaign and will be introducin you and expecting you to organize the council of elders—"
"Me? Didn nobody ask me nuthin. You mean Nisi? She change her name?"
"Well, Norton was supposed to tell you about it. Nisi wants to introduce you and then encourage the older folks to form a Council of the Elders to act as an advisory—"
"And you going to be standing there with your boobs out and that wig on your head and that hem up to your ass. And people'll say, 'Ain't that the homy bitch that was grindin with the blind dude?"
"Elo, be cool a minute," say Task, gettin to the next finger. "And then there's the drinkin. Mama, you know you can't drink cause next thing you know you be laughin loud and carryin on," and he grab another finger for the loudness.
"And then there's the dancin. You been tattooed on the man for four records straight and slow draggin even on the fast numbers. How you think that look for a woman your age?"
"What's my age?"
"What?"
"I'm axin you all a simple question. You keep talkin bout what's proper for a woman my age. How old am I anyhow?"
And Joe Lee slams his eyes shut and squinches up his face to figure. And Task run a hand over his ear and stare into his glass like the ice cubes goin calculate for him. And Elo just starin at the top of my head like she goin rip the wig off any minute now.
"Is your hair braided up under that thing? If so, why don't you take it off? You always did do a neat cornroll."
"Uh huh," cause I'm thinkin how she couldn't undo her hair fast enough talking bout cornroll so countrified. None of which was the subject. "How old, I say?"
"Sixtee-one or—"
"You a damn lie Joe Lee Peoples."
"And that's another thing," say Task on the fingers.
"You know what you all can kiss," I say, gettin up and brushin the wrinkles out my lap.
"Oh, Mama," Elo say, puttin a hand on my shoulder like she hasn't done since she left home and the hand landin light and not sure it supposed to be there. Which hurt me to my heart. Cause this was the child in our happiness fore Mr. Peoples die. And I carried that child strapped to my chest till she was nearly two. We was close is what I'm tryin to tell you.