The English that you are writing your narrative in is far from phonetic. If you can have silent letters in your words, so can your character. Also, the English language does not have a single sounds-to-symbols coding that is valid everywhere. A string of letters that represent one set of sounds in New Jersey will usually represent quite another set of sounds in Liverpool or Jo'burg. Two reasons why phonetic representation is a bad idea!
One can identify at least three levels: goin', goin, going. The first supposes a normative pronunciation and indicates that the speaker is not using it. This can be correct - for example, when the speaker is affecting a pronunciation they would not normally use, like Lord Peter Wimsey doin' his bally fool with an eyeglass act, don't you know? Whether this is in good taste (a) in and (b) outside the story is a matter requiring some care. It can also be used, in 1POV or close 3POV, to indicate that the POV character notices the speaker's accent: but this should (IMHO) be used very carefully.
The Uncle Remus approach uses it to indicate that the author thinks the character talks funny. This is (IMHO) bad writing. You are your characters' only spokesperson to the reader, and it is unprofessional to make fun of them. A peculiarly nasty example is the nonstandard spelling that does not represent a different sound. This has no possible meaning except to hint "IF Buddy tried to write this out, he'd get it wrong, ha, ha."
The second suggests to me that somebody - writer or speaker - is being deliberate about it. You want received pronunciation? Well, you listenin to the wrong guy. (Modern literary Scots is a weird special case here. As you can see from the link above, there has been a very deliberate effort to separate its orthography from that of "standard" English. What's come out is a semiconstructed language, like the fonetisized Inglish that Shaw championed for a while - and a cynic might postulate a tiebreaking rule, "in case of doubt, find out what the English are doing and do the opposite.") I would approach this one with great caution unless it's your own dialect.
I'd go with the third. Using dialect words is good - in measure. If a character says "wee" you may assume that they did not mean to say "little." Dialect sentence structures, done carefully, are wonderful - they, too, represent what the character meant to say. But use standard spelling - the character, speaking, does not intend to spell oddly!
In the comparatively rare case where the character is writing in nonstandard English, I think you have to go with how they'd spell it. But be careful - there's an Inspector Morse mystery where somebody is busted through forging a note that Morse recognizes as based on incorrect stereotypes of how semiliterate people spell. Research this one!