Learn Arabic (Modern Standard): أنا أعرفه.

In Arabic, object pronouns like "him" or "her" are attached directly to the end of the verb. Here, the suffix ـه means "him". So, أعرف (I know) becomes أعرفه (I know him).

Since the verb already means "I know", do we really need the word أنا at the beginning?

No, it is not strictly necessary. Arabic verbs already include the subject in their prefixes, so you can just say أعرفه to mean "I know him". Including أنا just adds a little emphasis, like saying "As for me, I know him."

How would I change this to say "I know her"?

You would change the attached object pronoun at the very end of the verb. The suffix for "her" is ـها, so "I know her" would be أنا أعرفها.

How is the end of the word أعرفه pronounced?

It is pronounced "a'rifuhu". The present tense verb أعرف ends with a short "u" sound, and the attached pronoun ـه is also pronounced with a short "u" sound here.