Quick glance

Ed Smith’s house, the Smiths, the Smiths’ house.

But when name ends in s or z:

Ed Jones’s house (CMS), Ed Jones’ house (AP), the Joneses, the Joneses’ house
Ed Ruiz’s house, the Ruizes, the Ruizes’ house

Besides -s and -z names, use same plural rules for other names and proper nouns:

and the Kellys, the Menlos, the Miglinis, etc.
two Jennys, two Germanys, two St. Louises, two Katzes

But possessive rules diverge a bit:

Kansas’s farms (CMS), Kansas’ farms (AP)
BUT the United States’ farms (because plural word is used as singular: the United States is, not are).

Possessive common nouns:

the dress’s fabric, the dresses’ fabric

BUT if next word starts with s:

CMS treats it normally: the dress’s stitching
But AP says the dress’ stitching because stitching starts with s
Both agree on normal plural: the dresses’ stitching

Deeper details

Plurals of names and proper nouns

Most names, add s

the Smiths, the Cases, the Nasrs
the Bradys, the Cavallos, the Morellis

Ending in s or z—add es

(also, j, x, ch, or sh sounds)

the Stevenses, the Joneses, the Hesses, the Rojases
the Gonzalezes, the Katzes
the Foxes BUT the Deverauxs (x sound vs. silent x)
the Churches BUT the Brachs (soft ch sound vs. k sound)
the Rushes

Same plural rules for other proper nouns

two Marias, two Joes, several Jennys in the class
two Kansas Citys, two Germanys, I love Thursdays
two St. Louises

Possessives of names

Most names, including ending with vowel or y

Add ’s for possessive, s for plural, and s’ for possessive plural.

Ken Smith’s house
I know the Smiths, the Smiths’ house

Jan Cavallo’s house
I know the Cavallos, the Cavallos’ house

Jed Kelly’s house
I know the Kellys, the Kellys’ house

Names ending with z

Add ’s for possessive, es for plural, and es’ for possessive plural.

Kim Gonzalez’s house
I know the Gonzalezes, the Gonzalezes’ house

Names ending with s

For possessive, CMS adds ’s but AP adds just ’  For plural add es, for possessive plural add es’

Ann Stevens’s house (CMS)   Ann Stevens’ house (AP)*
I know the Stevenses, the Stevenses’ house

*AP uses s’ for possessive proper names ending in s. However, their rule for possessive common nouns ending in s is different. See below.

Possessives

Most words

• Singular words take ’s   the bird’s nest (1 bird)   the city’s streets (1 city)
• Plurals take s’   the birds’ nest (multiple birds)   the cities’ streets (multiple cities)
• Plural non-s words take ’s   the children’s voices

Words that end in s

CMS: For words ending in s, the rules don’t change.

• Singular words take ’s (the dress’s fabric, the campus’s activities, Texas’s farms, Mr. Jones’s chair, St. Louis’s streets)
• Plurals take s’ (the dresses’ fabric, the campuses’ activities=multiple dresses and campuses)

AP: For words ending in s, the rules are different for common vs. proper nouns, and if next word starts with s.

• For common nouns ’s (the dress’s fabric, the campus’s activities)
• but s’ if next word starts with s (the dress’ stitching and the campus’ stadium because next word starts with s)
• For proper nouns s’ (Texas’ farms, Mr. Jones’ chair, St. Louis’ streets)
• Plurals take s’  (the dresses’ fabric, the campuses’ activities=multiple dresses and campuses)

Plural word used as singular

If it sounds like a plural but would take a singular verb, add just ’

Use for a proper noun whose official name is in plural form.

(Not to be confused with a proper noun that merely ends in s.)

the airline is considering, airlines are considering, BUT American Airlines is considering.
one airline’s flights, many airlines’ flights, BUT American Airlines’ flights

the state is large, the states are large, BUT the United States is large
one state’s problems, many states’ problems, BUT the United States’ problems

the hill is steep, the hills are steep, BUT North Hills is a city
one hill’s trees, many hills’ trees, BUT North Hills’ mayor

Also, e.g., General Motors, Arlington Heights, Philippines (and other island groupings ending in s), etc.

Use for the study, science, or principle of something, when the word doesn’t have a singular form.

politics is a game BUT the politics are complicated
politics’ biggest problem

Measles is spreading across the country. BUT Her measles are improving. (Are is debatable here, though.)
Measles’ worst symptoms are . . .

also: economics, etc.

Sources: CMS 7.16, 7.19, AP 2016 p. 415, http://www.chicagomanualofstyle.org/qanda/data/faq/topics/PossessivesandAttributives/faq0043.html, https://apstylebook.com/ask_the_editors/4650