Learn Dutch: Zij is een vrouw.

You can tell by looking at the verb and the rest of the sentence! Here, the verb is is (is), which is singular. Also, een vrouw means "a woman" (just one). If the sentence meant "they", it would use the plural verb zijn, like this: Zij zijn vrouwen (They are women).

Could I use ze instead of zij in this sentence?

Yes, absolutely! Ze is the unstressed version of zij. You would use zij if you want to put emphasis on "she" (for example, "SHE is a woman"), and ze for just a normal, relaxed statement. Both are grammatically correct here.

How do I pronounce een in this sentence? Is it like the number one?

No, when een means "a" or "an", it is pronounced like "uhn" (with a short, relaxed vowel sound, similar to the "e" in the English word "the"). If you want to say the number one, it is written with accents as één and pronounced with a long "ay" sound.

Why does the v in vrouw sound a bit like an English "f"?

In Dutch, the letter v at the beginning of a word is often pronounced a bit sharper and breathier than in English, making it sound somewhere between an "f" and a "v". For the rest of the word, the ou combination sounds very much like the "ow" in the English word "now".