THAN v. THEN

THAN:  This is used to show comparison.  Something is more/less than another -- better, stronger, bigger, lesser, weaker, etc.  Example:
She is taller than that tree.
I like ice cream more than cake.
We are able to chop down more trees than the other team.
She is less able to complete the tasks than her sister.

THEN:  This is used to show consequence and sequence of events.  Example:
We picked up our groceries at the supermarket, then we went home.
He saw the opportunity, made his mind up, then took action.
I used to like violent films, but then my brother was shot during a robbery and now I don't watch them as much anymore.

They're, There, and Their

THEY'RE:  This is a contraction of "they" and "are."  Example:
Are you looking for the pencils?  They're in the box on the top shelf.

THERE:  This is an adverb that basically means in or at a certain place or moment.  Here are some examples of its use ...
She is there now.
He stopped there (at a certain point in his speech) when the audience began applauding.
My anger was justified there (when I saw someone being inconsiderate at the supermarket).
New York City?  We went there last week.

THEIR:  possessive pronoun.  Examples:
The people have a right to defend their freedom.
Everybody in the room became upset when their money was stolen.
We don't have to listen to them; their opinions don't matter.