Learn Turkish: O bir kitap. - That over there is a book.

In Turkish, for simple statements like "it is", "he is", or "that is", you often don't need a word or suffix for "is". Just saying O bir kitap (literally "That a book") is the completely normal way to say "That is a book".

Doesn't O usually mean "he", "she", or "it"? Why is it translated as "That over there"?

O is a very flexible word! It acts as the personal pronoun for "he", "she", and "it", but it is also the pointing word for "that" or "that over there" (something far from both the speaker and the listener). You can tell from the context that it means "that" here.

If I want to ask "What is that?" to get this answer, how do I say it using the question word ne?

You would simply ask O ne? (literally "That what?"). Just like in our statement, you don't need an extra word for "is". The answer simply replaces the question word ne with the thing itself: O bir kitap.

Does bir just mean "a" or does it mean the number "one"?

It means both! Bir acts as the word for "a" or "an", and it is also the number "one". In everyday sentences like this, it is simply translated as "a book".