There: (adverb) in a particular place or position
I saw your father over there, by the Food Court.
Look, there is Mary, waiting for us at the school.
Their: (possessive adjective) belonging to or associated with a group of people easily identified
We can't use their slogan, that would be cheating.
Their family goes to Disneyland every year over Spring Break.
They're: (contraption) contraption of they are
They're here already, is the table set?
They're exceptionally humorous, so don't take them too seriously.
How to Remember:
Just like all the other contraptions, "they're" is easy to place because all you do is put "they are" into your sentence. Use "there" when you are referring to a place, because it also has the word "here" in it, which is also a place. "Their" has the word "heir" in it, who is a person, so "their" must refer to people.
~Little Miss Grammar~