Learn Finnish: Minä olin harjoittelijana sairaalassa. - I was working as a trainee in a hospital.

This showcases the essive case, which you are learning right now! Adding the ending -na or -nä expresses a role or a temporary state. Here, it translates to "as a trainee". While saying olin harjoittelija is grammatically possible, using the essive emphasizes that this was a temporary role or position you held, rather than your absolute permanent identity.

The English translation says "I was working", but there is no verb for "working" in the Finnish sentence. Where did it go?

You do not always need a separate verb for "working" in Finnish when stating your profession or role. The sentence literally translates to "I was as a trainee in a hospital". When you use the verb olla (to be) together with a profession in the essive case, the "working" part is automatically implied by the context.

Why does the ending on harjoittelijana use an -a instead of an -ä?

This is due to vowel harmony rules. The word harjoittelija contains the back vowels a and o. Because back vowels are present, they pull the ending to the back vowel version -na instead of the front vowel version -nä. The neutral vowels e and i in the word do not affect this rule.

Why does the sentence use sairaalassa instead of sairaalalla for "in a hospital"?