Learn Farsi: آن هنرمند خوشحال است.

The word آن is placed directly before the noun هنرمند (artist) to mean "that artist". In Farsi, demonstrative words like آن (that) and این (this) always come right before the noun they are pointing out, exactly like they do in English.

Why does the verb است (is) come at the very end of the sentence?

Farsi typically puts the verb at the very end of a sentence. The structure here is Subject + Adjective + Verb. So, the subject آن هنرمند (that artist) comes first, followed by the state of being خوشحال (happy), and finally the verb است (is).

Why does the first letter of آن have a wavy line over it?

That wavy line is a special symbol used when the long "â" sound (like the "a" in "car") starts a word. It sits on top of the letter alef to tell you to pronounce it as a long "â" rather than a short vowel. It is essential for spelling آن correctly.

Is there a word for "the" hidden in this sentence?

No, and that is because Farsi does not have a word for "the"! However, using a demonstrative like آن (that) already makes the noun specific. You are talking about that specific artist, so no other words are needed to make it definite.