These three words are often used incorrectly too, just like it's and its, even by native speakers. Again, it's not very difficult to remember which is correct when.
They're is the short form of they are:
My parents have gone on holiday and they're in France today.
When students like a teacher, they're more likely to do well in the subject he or she teaches.
Their is a possessive word, just like its, or my:
My children always leave their toys all over the place.
The dogs ran towards their master.
There is an adverb of place; it means in that place. Think of it as an answer to the question "where?". Here are some sample sentences:
We didn't want to go there, but we had to.
Why did you put my book there?
Here's a sentence with all three words; note how they're (!) used:
They're there, and all their friends are with them.