The Basics

[1] Contractions

             It's (it is), don't (do not), can't (cannot), won't (will not), she'd (she would or she had), etc.

[2] Omitted numbers

             the class of '88
             Note: if you are using "smart quotes," the bottom of the quote should curl forward. Sometimes, with modern word processors, it is necessary to
             type a letter, then the apostrophe, then the desired number to generate the correct symbol. Then delete the letter.)

[3] Omitted letters (particularly slang)

             Hey billy, don't kill
'em.   
             Singin
' in the rain   

[4] To pluralize letters and words

             How many I's are there in Mississippi?
             I am telling you the do
's and don't's of punctuation.

Beyond the Basics

[5] To show possession

Note: we're getting into a notoriously sticky subject here. I'll first explain possession in accordance with the Chicago Manual of Style. Then I'll describe an
alternative. Which is correct? That depends on your editor. Neither is "wrong," but your editor may prefer one over the other. But as long as you are consistent,
neither style is incorrect.

[5A] Proper nouns (singular): to show possession, add "'s"

             Rob
's book
             Kevin James
's car
             Marx
's theory
             My aunt and uncle
's car. (Notice that only the last element of a noun unit takes the possessive case.)
             The resident assistant
's rules. (With compound nouns, the last element takes the possessive case.)
             Baby
's bed (one baby)
             Horse
's pasture (one horse)
             John Smith
's house  
             Dickens
's manuscripts

[5B] Proper nouns (plural): to show possession, add only an apostrophe (no "s").

             Babies
' beds. (multiple babies, multiple beds)
             The horses
' pasture (multiple horses)
             The Smiths
' house. (The families house)


Exceptions to 5[A] singular nouns. (When to leave off the final "s"):

             [A] "When the singular form of a noun ending in "s" looks like a plural and the plural form is the same as the singular, the possessive
                   of both singular and plural is formed by the addition of an apostrophe only."--
Chicago Manual of Style

                          politics' meaning
                          economics
' forerunners

             Note: Although the above examples are correct, the better solution is to recast the sentence using
of.
             
                          meaning of politics
                          forerunners of economics

             [B] Add an apostrophe only (no
s) when the last element of a name is a plural form ending in "s."

                          Rolling Hills
' residents (meaning: the residents of Rolling Hills)
                          the United States
' role in Iraq

             [C] Names of two or more syllables that end in an
eez sound, leave off the final "s."

                          Euripides
' tragedies
                          the Ganges
' source

             [D] Names or words ending in a silent "s." (leave off the final
s)

                          the marquis
' mother
                          Albert Camus
' novels

[6] Double possessives

             a car of Rob's  (In this case, Rob has more than one car)
             a friend of Kevin
's (Kevin has more than one friend)

[7] Idiomatic expressions/Genitive case

             For Jesus' sake
             For goodness
' sake
             hard day
's night
             a year
's wage
             heart
's desire
             a week
's worth
             an hour
's delay
             five days
' leave

Quick and Dirty Approach: If you don't want to get bogged down in all the rules, there is another acceptable option.
Please note: this does not conform strictly to
Chicago Manual of Style, but it is not technically incorrect.

If the singular noun (before being possessive) ends in "s" then only add an apostrophe (leave off the final "s"), otherwise, add "'s."
(Of course, if the noun is plural, you never add the "s.")

             Tom Jenkins
' (the house of Tom Jenkins)
             Dylan Thomas
' poetry

Syntax

The only syntactic concern is the auto-format of "smart quotes." Be sure the single quote curls forward at the bottom. This will be an issue in words that begin
with an apostrophe: 'em (them), 'er (her), etc. The trick (for most word processors) is to type a place-holding letter, then the quote, then the word, then go back
and delete the placeholder.   

Usage Key

Take a moment and consider if the word is singular or plural before making it possessive.

             baby
's vs babies'
             horse's vs horses'

Imprecise Use

Inanimate objects, unless being anthropomorphized (given human traits), should not be used in the possessive case. Not all editors strictly adhere to this, but it
is generally a good stylistic practice.

             <wrong> The house
's roof.
             [correct] The roof of the house.


Misuse

"It's" is a contraction of "it is." "Its" is a possessive pronoun (like his or hers).

             It
's a cold day. (It is a cold day.)
             The horse had its saddle on. (possessive: the saddle of the horse)
Apostrophe  (')
(An apostrophe is the same symbol as a closing single quote.)
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