Trask writes that possessive apostrophes are the most troublesome of apostrophes, and apostrophes are the most troublesome of punctuation marks. (I think commas must give apostrophes a run for their money.)

The basic rule for possessive forms is that ’s is added to the end:

Henry's book

If the noun ends with s, the same rule usually applies:

Charles's shoe

The first exception is for a plural noun that already ends in s:

my parents' holiday
the ladies' bathroom

These words are not pronounced with an extra iz sound, and so we don’t indicate an extra s in writing.

This brings us to the second exception. If the possessive form of a noun ending in s is not pronounced with an extra s, it only takes an apostrophe:

Aristophanes' plays
Bridges' marmalade

The final exception is for pronouns:

Whose is this? 
The essay is hers

But this does not apply to possessive indefinite or impersonal pronouns:

one's conscience
someone's lunch

I have previously covered its as a possessive form, and it is perhaps the pronoun most commonly incorrectly assigned an apostrophe.

Fowler’s Dictionary of Modern English Usage gives a comprehensive breakdown of exceptions and usage in more complicated situations, and I highly recommend it if you are worried about using apostrophes correctly.