Learn Farsi: چند تا کتاب داری؟ - How many books do you have?

In Farsi, whenever you use numbers or ask about quantities with words like chand (how many), the noun that follows must always be in the singular form. So, you literally ask "how many book" instead of "how many books".

What is the purpose of the word ta after chand?

ta is a counter word, similar to saying "pieces of" in English, though we usually don't translate it. In spoken Farsi, it is almost always added after numbers and after chand when counting physical things.

Could chand mean anything else besides "how many"?

Yes, if this were a normal statement instead of a question, chand or chand ta would mean "a few" or "several". Because this is a question, it translates to "how many".

How do we know it means "do you have" if the word for "you" (to) isn't in the sentence?

Farsi verbs change their endings to show who is doing the action. The -i ending on the verb dari specifically means "you" (informal, singular). Because the verb already gives this information, the pronoun to is usually dropped in everyday conversation.