Question

What are the reasons to use an apostrophe?

Answer 1

Grammatically, when something is possessive, and only when something is possessive. In literature, when a character is musing on something, basically.

Explanation:

Add ['s] to the end of a word/name that doesn't end in s to make it possessive. (Sally's tugboat.)
Add [s'] to plural words to make them possessive. (The (multiple) brigadiers' uniforms.)
The way I learned it, if a singular noun ends in s and has one syllable, add ['s], but if it has more than one, only add [']. I have seen elsewhere that you either always add ['s] or always only add ['] so I guess you make your call there. (Ms. Jones' or Ms. Jones's property.)
NEVER USE AN APOSTROPHE TO MAKE SOMETHING PLURAL.

An apostrophe is also a literary feature where the speaker addresses some absent presence, and since you were ambiguous on what you wanted, I'll just tell you about it. You use an apostrophe when your character is being dramatic, having a monologue, and/or musing. See James Joyce's A Portrait of the Artist as a Young Man: "Welcome, O life!" or Mary Shelley's Frankenstein: “Oh! Stars and clouds and winds, ye are all about to mock me; if ye really pity me, crush sensation and memory; let me become as nought; but if not, depart, depart, and leave me in darkness.”