Learn Finnish: Hän on ilahtunut vieraasta. - He is delighted by the guest.

This is the core rule for emotion verbs! Verbs expressing a reaction or emotion, like ilahtua (to become delighted), require the cause of that emotion to be in the elative case (-sta/-stä). While in English you are delighted "by" or "about" something, in Finnish you are delighted "out of" it.

On ilahtunut looks like the perfect tense. Why is the translation "is delighted" instead of "has delighted"?

Ilahtunut is the NUT-participle of the verb ilahtua (to get or become delighted). While it is used with the verb "olla" to form the perfect tense ("he has become delighted"), it frequently acts just like an adjective describing a current state of mind. Therefore, hän on ilahtunut naturally translates to "he is delighted".

How does the word vieras (guest) change into vieraasta?

Nouns ending in -as or -äs belong to a specific word group. When adding a case ending, you drop the final -s and lengthen the vowel before it to build the stem. So vieras becomes the stem vieraa-, and then you attach the elative ending -sta.

Is the verb ilahtua related to the word for happy (iloinen)?

Yes! Both words come from the root noun ilo (joy). The verb ending -tua often implies a change of state (meaning "to become [something]"), so ilahtua literally translates to "to become joyful" or "to get delighted".