These three words are homophones, which are pronounced the same but have different meaning and spelling. As a result, usage can be confusing. But they’re easy enough to differentiate and set to memory.
“They’re” is a contraction of “they are.” For example:
They’re angry I moved to Cincinnati.
I’m not convinced they’re going to succeed.
If you’re not sure whether you’ve used “they’re” correctly, replace it with “they are.” If the sentence works, you’re in the clear.
“Their” is a possessive pronoun that indicates something belongs to them:
My neighbors have lost their dog.
Their garden is beautiful.
“There” often refers to place:
She needs to stand right there.
It must be exciting to work there.
It can also be used as an introductory subject:
There are many people waiting for the bus.
Sometimes it is an interjection. Here, it expresses satisfaction:
There, the paint is dry.
Any time you use one of these words, double check that you’ve made the right choice. While many misuses happen because the author doesn’t know the differences, others are a result of carelessness.