There, their, and they're are three different words, pronounced the same but spelled different. They are homonyms. So, where to use which?
Since I'm good with helping others with word associations I have been asked to please share.
There: notice that the word here is in there. So, it's not here, but there.
Their: notice that the word heir is in their. So, they (each being an heir) inherited the house and it is now their house.
They're: notice the apostrophe. This means that a letter---or letters--has been omitted. In this case the letter a. In full it would be they are.
Other words with apostrophes are jack-o'-lantern, o'clock, O'Leary, ma'am, etc. which indicate that a letter--or letters--has been omitted.
Thus, there: not here, but there.
their: each an heir so their house.
they're: omitted letter, a in this case. Also, if the other two don't fit, it must be this one. :)
Then there is it's and its.
It's has an apostrophe, so an omitted letter, in this case i (it is) or ha (it has).
It's raining = it is raining. It's rained = it has rained.
Its is a rare possessive as it doesn't have an apostrophe like Jim's books, boys' bats, or deer's tail.
If a letter has been left out, (it's), then use this word. If showing possession, then use its.