Learn French: Tu es fatigué, je te recommande une vitamine. - You are tired, I recommend a vitamin to you.

In French, object pronouns like te (to you) almost always go directly before the verb. So instead of saying "I recommend to you" like in English, you say je te recommande (literally: "I to you recommend").

How do I know te means "to you" here, rather than just "you"?

It depends on the verb! In French, you recommend something to someone (recommander à quelqu'un). Because of this "to" relationship, te is an indirect object pronoun here, meaning "to you."

If I am speaking to a woman, does the sentence change?

Yes, but only the first part. You would add an e to the adjective to make it feminine: Tu es fatiguée. The pronoun te does not change at all, because me, te, nous, and vous are exactly the same for both masculine and feminine.

Is the word vitamine similar to English?

It looks very similar, but remember that it is a feminine noun in French (une vitamine). Also, because of the silent e at the end, the letter n is fully pronounced, making it sound like "vee-tah-meen."