The pronunciation of the suffix "s" added for a possessive can have three forms: [s],[z] or [iz].
The rules for pronunciation are the same as for the plural. You have:
[s] Nick's Pope's Stuart's (voiceless consonant before s)
[z] Laura's Greg's Tom's (voiced consonant or vowel before s)
[iz] Travis's , Buzz's , princess's, coach's (when the singular words end up in "s","z" or fricatives such as "sh", "ch","ge")
Source: The pronunciation of English, Charles Kreidler
Note: Only the singular words add the possessive "s". The absence of possessive "s" after a plural is for the ease of pronunciation, as exemplified below.
If a man with two mistresses wanted to speak of things he'd given to both of them, I'd advise him to drop the 's, rather than try to pronounce mistresses's with a straight face!
Okay, some hearers might then think he only had one mistress. But that might even be an advantage - if one of the mistressess overheard him talking about the gift[s], for example.
The possessive s is dropped from writing in many contexts, but there's no universal agreement about exactly which. Take James's, where quite a few people drop that last s in writing. But very few people would fail to pronounce it - especially not parents of James! Unless maybe if they're talking about James's essay, for example. Even then I would think it slightly odd to drop the s because it's not that hard to say. YMMD, of course.
However, if the possessive is not added, so we have only James', the word is pronounced (in careful speech) exactly as if it were by itself. In other words, the possessive doesn't make a difference.
(the above answer was merged from the ones provided by FumbleFingers and Bogdan Lataianu)