Learn Finnish: Hän sanoi, että hän suhtautuu opiskeluun vakavasti. - He said that he takes studying seriously.

This is because of the verb suhtautua (to relate to, to take an attitude toward). Verbs of reacting and committing in Finnish often require the thing you are reacting to to be in the illative case.

The translation says he 'takes' studying seriously, but doesn't the verb ottaa mean 'to take'? Why use suhtautua here?

Ottaa is mostly used for physically taking something. When you mean 'take' in the sense of having an attitude towards a concept or situation, Finnish expresses this with the verb suhtautua paired with the illative case.

Why is suhtautuu in the present tense when the main verb sanoi is in the past tense?

English uses 'backshifting' in reported speech, changing the reported verb to the past tense to match the main verb (e.g., 'He said he took...'). Finnish usually keeps the tense of the original quote if the statement is still true. Since he originally said 'Suhtaudun opiskeluun vakavasti' (I take studying seriously), the present tense is kept.

Why do we use vakavasti instead of the basic adjective vakava?

Because it describes the verb suhtautuu, not a noun. Just like in English, we need the adverb form vakavasti (seriously) rather than the adjective vakava (serious) to describe how an action is performed.