I'm not a fan of non-standard spelling to convey dialect (that's SO 19th Century). It's confusing, and often discriminatory (why spell certain speakers' words phonetically and not others, when English spelling is not phonetic?).
But how then do we convey when a speaker or a POV character have a distinctive way of speaking? Let's say she's Irish, or from Chicago, or he's a 2nd Century Roman warrior?
First, I think, we have to do our research. We have to get enough experience with the rhythm of this speaking culture's sentences and the lingo to convey it accurately. But then, we should cut back (usually). Even without spelling irregularities, "authentic" dialect can put off readers. After all, that Roman warrior spoke Latin. We're already "translating" his speech into English, so we want to give a flavor without choking the reader.
I've been thinking of what constitutes a flavor. First, the rhythm of the sentences can give a flavor of the speaker's culture. There's an old book called English as We Speak It in Ireland which gives examples of sentences only an Irishperson would say:
I went to town yesterday in all of the rain, and if I didn't get a wetting, there's no cottoner in Cork. (That is, he got wet.)
An illigent song he sang, I'll go bail.
The author (PW Joyce) remarks that Irish English uses negation (if I didn't), stock phrases (I'll go bail), and reverse order (putting the object first -- An illigent song he sang) for emphasis. This is not a dialect that honors Struck and White's edict to "use no unnecessary words," or rather, the Irish don't think there are unnecessary words!
Read in the vernacular to pick up the sentence rhythm. Watch films and TV shows =made= (not just set) in the culture. For historical settings, read books written then (you might have to read in translation, of course) or plays that would have been performed then.
(The British filmmakers, you know, are famous for making everyone else, especially Romans, sound English. Not just speak English, but sound it. All the rich Romans sound like Lord Olivier, and all the poor ones sound Cockney, like the Artful Dodger.)
But also, there are certain words or types of words that can be used without confusing the reader or making the character opaque. Here are some I've thought of, but please add!
Variations of "you". This, far more than "I", for some reason, marks a dialect quite precisely. Any linguist who hears "youse" knows the speaker is from the Great Lakes-Midwest (probably Chicago). "You-uns" is Pennsylvanian.
What others have you heard? When would you use them? What about our Roman warrior, who doesn't speak English, but must be presented as speaking English?
Curses and other angry expletives: Even if the reader doesn't know what the word means, the placement and the context will make it clear that "glupak!" is a curse word. Spelling can distinguish dialects when you're dealing with English speakers:
Wonder words: These are words that seem to erupt spontaneously, and because they're spontaneous, they're going to give a sense of the character's background. You can do this is the actual language if the character is foreign. Examples: