Learn Romanian: Nu știu.

In Romanian, the verb ending usually tells you who is doing the action, so you don't need to use subject pronouns like "I" (eu) or "you" (tu). Știu already means "I know." You would only add eu (eu nu știu) if you really wanted to emphasize that you don't know, contrasting yourself with someone else who might.

How does negation work here? Is there a word for "don't"?

Romanian makes verbs negative much more simply than English. You just put nu (no/not) directly in front of the verb. There is no equivalent to the English helper verb "do" or "don't."

Can I use știu to say I don't know a person?

No. Romanian has two verbs for "to know." Use a ști (the verb in this sentence) for knowing facts, information, or how to do something. If you want to say you don't know a person or a place (meaning you are not familiar with them), you must use the verb a cunoaște.

How do I pronounce the ș and the -iu at the end of știu?

The letter ș sounds like the "sh" in the English word "shoe." The ending -iu sounds a bit like "ew", making the whole word sound very close to "shtew" in English.