This could actually be an enormous topic, but I'm going to stick to small details here. I got this idea from the article I posted yesterday (here) about University of Kansas and their upcoming production of A Midsummer Night's Dream that will be executed in all original Shakespearean pronunciation.
First of all, I think it's really cool that linguists are able to reconstruct the pronunciation of the time, and even cooler that this can be used for theatrical purposes. When you listen to the snippets provided in the article, you really get the sense that this dialect is related to Cockney and to Australian (which it is, as a sort of distant parent). Another interesting point made in the article is that this language was not what we'd consider refined-sounding, unlike the more recent British renditions of it. I could totally see Shakespeare's ribald jokes coming through hilariously in the accent as it was rendered by the young actors at KU.
The other thing this shows me is how pronunciation and delivery style are lost when the language is written down. I'd been told that Shakespeare's plays were best seen on the stage rather than read silently, and I've always agreed with this - it only becomes more evident when we see how it used to be pronounced. It was real fun, for example, to see that the rhymes Shakespeare used were not nearly as approximate in his time as they appear to be in ours. Word really DID rhyme with sword.
This disconnect between the pronunciation/delivery and the written word is something we all run up against when we write stories. It's a challenge whether we are dealing with dialects of English or alien and fantasy languages. We can spend lots of time designing a language, or we can imagine the English pronunciation and delivery that a person has, and imagine that as conveying part of their character. However, that information is much harder to render in written form. Do we alter spellings in dialogue to suggest pronunciation? Do we provide reactions from surrounding people to give evidence of this person's dialect? Do we alter dialogue tags? All of the above?
In this instance I think that the example of Shakespearean English gives us some good hints for what to do. Not one of us would ever pick up a Shakespeare play and say, "I can't tell that these people are speaking differently from us." It's in the words - the vocabulary, the pronouns. It's in the turns of phrase. It's in the way that the people in the plays talk about the world around them. These are the very same tools that we can use for our own characters.
In linguistics it's typical to think of linguistic objects as having features. For example, for vowels, there are the features of height, front/back, and roundness. I think the idea of features is a good one for the portrayal of dialects and speech styles in writing as well. Sit down and think about the speech of your character, and write down its most salient characteristics. "This person always uses contracted phrases like gonna," might be one example. Since a habit of speech like this is typically going to be used throughout a book (unless it's My Fair Lady), it's a very good thing to include in a book/world bible or a guide to the characters in a series. Wherever you keep your notes on characters' appearance and their habits of dress or nervous tics, include a list of the major features of their language use. That way when you need to write dialogue for them, now or in the future, you'll have a reference to go back to.