The incorrect use of the words "there, their, or they're" is a special pet peeve of mine. This is a common error that can be easily addressed and, while proper usage doesn't garner any attention, improper use can make your writing incomprehensible. So - simple rules to follow:
Are we talking about ownership of an object? (house, dog, place, movie, etc.? ) Use THEIR
ex: That dog is their dog.
Are we indicating where an object is located? (on a table, in a corner, etc) Use THERE
ex: That dog is over there, in the corner.
Are we indicating what someone is doing? (going to the store, the museum, etc) Use THEY'RE which is a contraction of the words "They are".
ex: They're walking the dog in the morning.
A little memory trick - They're walking their dog over there.
Remember, just because words sound the same doesn't mean they have the same meaning. A few seconds to determine the proper spelling saves you a lot of grief in the long term.