The apostrophe is used in two main ways.
The omission apostrophe
This usage shows that letters have been taken out of a word or phrase to shorten it. Omitting letters in this way is generally appropriate in informal writing or writing intended to be spoken aloud.
could not becomes couldn't
should have becomes should've
it has becomes it's
will not becomes won't
The apostrophe always goes where the letters have been taken out. It is worth noting that, in some cases, words can be shortened in irregular ways but an apostrophe should still be inserted. For example, will not becomes won't.
The possession apostrophe
An apostrophe can also be used to show that something belongs to or is connected with something else.
the dog's bone
the company's logo
The apostrophe is usually placed before the 's' when something is connected with one person (singular). However, if there were two dogs or more than one company (plural), the apostrophe would be placed after the 's'.
the dogs' bones
the companies' logos
For words which already end in the letter 's', it is technically correct to add an apostrophe and an extra 's'.
For example, Jones's Bakery or Thomas's car.
It's and Its:
Be careful with these two words as they can be confusing when it comes to apostrophes.
It's is a shortened version of it is.
Its is a possessive pronoun and does not have an apostrophe.
The owner took his dog for its walk.