I often see these mixed up, even though it’s very easy to tell which to use when.

1. There refers to a place, as in “Put it there.” It’s also used to declare the existence of something, as in “There are four people here.”
2. Their is a possessive pronoun, conveying the idea that something belongs to them. For example, “It is their money,” or “The house is theirs.”
3. Finally, they’re is a contraction to replace “they are.” Use it like so, “They’re going as soon as they get permission.”