Their shows ownership. There points to a place or starts a sentence. They're is they are. Their scores. There on the desk. They're ready. Diction as a set is in word choice.
Expand the contraction
If they are fits, use they're. If something belongs to people, use their. If you can point, use there. They're books is wrong unless the books are people.
To versus too is the same kind of look-alike, in to versus too. Your versus you're is in your versus you're. Grammar overall is in ACT grammar rules.
The bottom line
Ownership: their. Place or opener: there. They are: they're.
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