When should I use their or there?

THEIR is a possessive pronoun. Examples:
Their house is the brick house on the corner.
Have you seen their dog?
We asked the children to pick up their toys.

THERE is usually an adverb. It may mean a place or it may introduce a sentence.
Examples:
I live over there.
There are thirty students in this classroom.

When should I use a apostrophy (s')?

This site has a great explanation and examples of apostrophe uses.

http://owl.english.purdue.edu/handouts/grammar/g_apost.html

There's is a contraction for there is..as in

There's a bug in my soup.

There's a right turn ahead at the orchid shop.

There's something about Mary.

To use "their" correctly, you should use it as a possessive pronoun to show ownership or belonging. For example, you can say "Their house is the brick house on the corner," indicating that the house belongs to them. Another example is "We asked the children to pick up their toys," where "their" shows that the toys belong to the children.

On the other hand, "there" is typically used as an adverb to indicate a place or to introduce a sentence. For instance, you might say "I live over there," pointing to a specific location. Alternatively, you could say "There are thirty students in this classroom," using "there" to indicate the existence or presence of something.

To determine when to use an apostrophe (') in a word, you need to consider its purpose. An apostrophe is commonly used in contractions to replace omitted letters. For example, "there's" is a contraction of "there is." It is used to indicate the existence of something, as in "There's a bug in my soup" or "There's a right turn ahead at the orchid shop." It is important to note that contractions are more commonly used in informal writing or speech.

If you want more detailed information and examples of apostrophe usage, you can visit the website owl.english.purdue.edu/handouts/grammar/g_apost.html.