The apostrophe 's to denote possession is also known as 'Saxon genitive', which originated from Anglo-Saxon, also known as Old English. The fact that English is the only language to use this form of spelling makes it difficult for learners. The purpose of this post is not, however, to explain the rules governing the use of the possessive 's. For that, I'd suggest looking at your favourite grammar book.
Singular noun not ending in '-s'
This is straightforward. We just add 's to a singular noun.
my wife's bicycle
my friend's computer
Max's mobile phone
Spain's economic crisis
Regular plural nouns
This is also straightforward. We add the apostrophe at the end.
their sons' school
her parents' business
the girls' boyfriends
These get an 's just like singular nouns.
the children's video games
Nouns ending with -s
Here, we can either add 's or just an apostrophe at the end. It is said that adding 's is a more common procedure. Some follow the rule of adding 's if it's a singular noun and only ' if it's a plural noun.
Charles' wife OR Charles's wife
Steve Jobs' death OR Steve Jobs's death
Doris' iPad or Doris's iPad
It is worth pointing out the pronunciation rules though. The ending '-s is pronounced just as in that of plurals.
St. James's Park /seɪnt ˈdʒeɪmzɪz pɑːk /