possessives

[DamianWarS]

to show the possessive in a noun you commonly use the apostrophe s affixed to the word. For example "the house of the dog" would be "the dog's house" However I get confused with some forms of showing possession and wanted some things cleared up. Here are some examples:

"My car is broken and theirs is not."
What this sentence is really saying is "My car is broken and their car is not". But we like to shorten things up because the subject "car" doesn't need to be repeated and is assumed in the second instance so we replace the whole subject with just the added "s" as a possessive for the pronoun "their". But the problem is "their" already has the possessive apart of the word so we don't need to add a possessive so it seems adding "s" is redundant. So what is correct here? Should we be saying "their is not" or "theirs is not" or should we not remove the subject and say "their car is not".

When do you add an apostrophe s or just "s" or just an apostrophe to indicate a possessive and how is it spoken?
From what I understand when a noun ends in a "s" you don't add an apostrophe "s" for the possessive you just put an apostrophe. For example the possessive plural of "dog" would be "the dogs' house" Or the possessive of a word ending in "s" like the person's name "Douglas" would be "the Douglas' house" I think I am correct with the above but how are they spoken? Is it Douglas or Douglas-ez and or is it dogs or dogs-ez. To me Douglas-ez seem correct but dogs-ez seems incorrect but how to I justify one over the other? Do you omit the "ez" affix when its on a plural noun and add it when its on a singular noun ending in "s" or is this wrong altogether and you should never add "ez" to the end of words.

[Beeesneees]

'... theirs is not' is correct for the reasons you gave. The possessive is included in 'theirs'.

The possessive of the house of the dog is the dog's house (note the position of the apostrophe). This is singular. If there were more than one dog, both in the same house then The dogs' house would be correct. If there were more houses then the dogs' houses would be correct.
In each case, the pronunciation is 'dogs'.

Douglas's house = the house of Douglas. This is pronounced 'Douglas-ez'
You have no doubt seen or heard about a requirement to drop the 's' after an apostrophe for a word which naturally ends in 's'. However, the only reason to apply this rule for a word naturally ending in 's' is where it is difficult to pronounce s-ez for some reason.
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Cheers m' dears!

[DamianWarS]

[Beeesneees]

'Theirs' is the third person plural possessive pronoun (which stands alone) - it replaces "their" + noun
This rule also applies in other cases. None of the possessive pronouns have an apostrophe.
Compare:
This is their home. This home is theirs.
This is her home. This home is hers.
This is our home. This home is ours.
This is your home. This home is yours.
This is my home. This home is mine.
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Cheers m' dears!