There are different ways to show ownership of something. To show possession you can use nouns to modify other nouns.
(For purposes of clarity, we distinguish between the genitive case and the possessive case here.)
The good news is that the genitive case "of" is used less and less in English today. Hooray!
The possessive case is used to show ownership. The possessive pattern or mark ('s) is generally used when indicating a relation of ownership or association with a person, rather than a thing. (Linguistically speaking it is a form of genitive case.)
Singular nouns take -'s.
Lynne's web site kept growing larger and larger.
There are, as ever, exceptions to this rule. When a group of people is involved or animals.
The members' forum.
The dogs' tails.
Companies are often treated like people.
Coca Cola's latest advertising campaign.
Irregular plural nouns that don't end in s take -'s.
The children's toys.
The people's court.
Plural nouns that end in " s " take an apostrophe at the end ( ' ).
The girls' dresses.
People's names that end in "s" you can write (') at the end, or add ('s).
Charles' job was on the line.
Charles's job was on the line.
Try to avoid sounding like hissing Sid though. When an added - s would lead to three closely bunched s or z sounds just use an apostrophe at the end.
The map of Ulysses' journey.
If you have to show joint ownership, give the possessive form to the final name only.
Abbott and Costello's famous baseball sketch.
Pronouns and determiners are inflected to show the possessive / genitive case.