I like the Prentice-Hall "Handbook for Writers" because their directions are simply stated.
Supposedly we learned the rules in school, but watching the sky outside the room, or dipping pigtails in inkwells was more interesting.

The APOSTROPHE (extracted)
Brief enuf' t' tape t' yer PC. (or is that en'uf' ?) (or jes' enuf?)

Use an apostrophe to show the possessive case of nouns and indefinite pronouns.
1. If the word does not end in s, add an ' and s to form the possessive
the woman's book, the women's book, people's books
2. If the singular of a word ends in s, add an ' and s unless the second s makes pronunciation difficult; in such cases, add only the '.
Lois's car, Moses' leadership
3. If the plural of a word ends in s, add only the '.
The girls' locker room, the Smiths' house
4. In compounds, make only the last word possessive
father-in-law's pipe, mothers-in-law's birthdays, someone else's fault
5. In nouns of joint possession, make only the last noun possessive; in nouns of individual possession, make both nouns possessive.
John and Paul's office
John's and Paul's offices

A table of singular and plural possessives
child   child's   children   children's
passer-by   passer-by's   passers- by   passers-by's
etc.

Use an apostrophe to indicate the omission of a letter of number.
doesn't does not; it's it is;
blizzard of '89 blizzard of 1889
will-o'-the-wisp will of the wisp; o'clock of the clock

In reproduction of speech- dialect, colloquial.
"An' one o' the boys is goin' t' be sick," he said.
[Anyways, it don' make no nevuh mind no ways- added for Open Mike]

Use an ' and s to form the plurals of letters, numbers, and words used as words.
Cross your t's and dot your i's.
The 1970's were known as the 'me' decade. ['70's]
Eliminate unnecessary and's.
These are the only kinds of situations in which the ' is used in forming plurals. It is never used in forming the plurals of proper names or other nouns.

Do not use the ' with the possessive forms of personal pronouns
his father, an idea of hers, a friend of theirs.

Be careful not to confuse the possessive pronoun its with the contraction it's (it is).