I know the three "there's" can be intimidating, but THERE are some easy tricks to learn that will help you choose:
(1) "There" is an adverb and is used when you are talking about location. If you notice, I already used it up THERE in the first sentence. If the loacton trick isn't working for you, check to see if you can say "is" or "are" after it. THERE ARE no other forms that can have "is" or "are" after it (see what I did THERE...).
(2) "Their" is a possessive pronoun and is used to show possession by other people. You use it to indicate something belongs to them. Once I tell people this rule, it's THEIRS to use. Then , any fears they have about grammar are THEIRS to lose!
(3) If you can substitute the words "they are," then you need to choose "they're." This form is a contraction and THEY'RE people who are really good at using it. Even though saying "there are" is more formal, THEY'RE still people who choose this informal option.
THERE you go! Good luck!!