Learn Dutch: De vrouw is hier. - The woman is here.

Dutch has two words for "the": de and het. Every noun uses one or the other. Vrouw (woman) is a "common gender" noun, so it always takes de. A helpful rule of thumb for beginners: nouns that refer to adult people (like woman, man, mother, father) almost always use de.

Is the Dutch word is exactly the same as the English word "is"?

Yes, it works exactly the same way here! Is is a form of the Dutch verb zijn (to be). Because de vrouw (the woman) acts as a "she", we use the third-person singular form, which is is.

If I wanted to replace de vrouw with a pronoun to say "She is here", which one would I use?

You would use zij or its unstressed form ze (she). The sentence would become Zij is hier or Ze is hier.

How do you pronounce the vowel part of vrouw?

The ou combination in vrouw sounds a lot like the "ow" in the English word "cow" or "now".