it’s – its

It’s with an apostrophe is short for it is. The short form is not used in formal writing:

It’s raining.

Its without an apostrophe is a possessive pronoun:

The Academy will hold its next meeting in Boston.

who’s – whose

Who’s is short for who is and is not used in formal writing:

Who’s responsible for this?

Whose means of whom or of which:

Novak, whose recent paper on …

you’re – your

You’re is short for you are and is not used in formal writing:

You’re wrong!

Your is a possessive pronoun:

Your paper has been accepted for publication.

we’re – were – where

We’re is short for we are and is not used in formal writing:

We’re hungry!

Were is the plural of was:

We were very surprised at the results: they were completely unexpected.

Were is also used with you, whether singular or plural:

You were right, Professor Clever Clogs.
Professor Clever Clogs and Dr Smarty Pants, you were both wrong.

Where means at which place:

Where are you giving your paper?

they’re – their – there

They’re is short for they are and is not used in formal writing:

They’re off!

Their is a possessive pronoun:

Watson and Crick made their breakthrough in Cambridge.

There means that place:

We should go there one day.

There is also used in there is and there are:

There are several possible explanations for …