Most writers are quite clear about how to use apostrophes with possessives:
Singular nouns— for most nouns, the possessive is simply made by adding an apostrophe followed by an s:
The mustachioed man’s chickens have laid their eggs.
Plural nouns — except for a few irregular plurals* that don’t end in s, the possessive is made by adding an apostrophe after the s:
Many of his chickens’ eggs are ready to hatch.
* For example: Many mustachioed men’s favorite egg-dish is the humble omelet.
But in my experience, there is a great deal of confusion when it comes to proper nouns, particularly names ending with s, and since many writers—particular those who write fantasy!—tend to choose names that end in s, x, or z, this issue arises frequently when I am editing.
The general rule** is that for (most) proper nouns, and this includes nouns that end in s, z, and x, the possessive still takes an apostrophe followed by an s.
Cortez’s gold fillings
Jimi Hendrix’s hairy knuckles
Karl Marx’s moustache
Robbie Burns’s sideburns
The Williamses’ washboard abs (Everyone in that family is an exercise nut!)
The Higganbothams’ horrible halitosis (Mr and Mrs Higganbotham are, sadly, both sufferers. Probably just as well).
Of course with every rule in the English language, there are exceptions happy to confound the unsure. The Chicago Manual of Style (7.18 – 7.22 15th Edition) gives lots of lovely examples including:
For Jesus’ sake but Jesus’s contemporaries
Also: Euripides’ tragedies (“a name of two or more syllables that ends in the eez sound”)
Decartes’ three dreams (“singular words and names ending in an unpronounced s”)
Confused? I suggest you follow the general rule… or you could just use of, such as the dandruff of Dickens and the sneezes of Strauss.
** According The Chicago Manual of Style, the fiction editing standard.