Learn Dutch: De auto is ook groot. - The car is also big.

When an adjective comes after the verb (like is here), it never gets an extra -e at the end. You only add the -e when the adjective comes directly in front of the noun, like in de grote auto (the big car).

Can I put ook at the end of the sentence, like "The car is big too"?

No, in Dutch, short adverbs like ook (also/too) usually stick close to the verb. In a simple sentence like this, it comes directly after the verb, so it must be De auto is ook groot.

How do you pronounce the au in auto?

The au combination in Dutch makes a sound similar to the "ow" in the English word "cow" or "how". So auto sounds a bit like "ow-toh".

Is there a rule to know that it is de auto and not het auto?

Unfortunately, no. While about 75% of Dutch nouns are de words, there isn't a strict rule to guess the gender of most words. You simply have to memorize the article (de or het) together with the noun when you learn it.