Learn Finnish: Isä hakee minut koulusta. - Father picks me up from school.

Minut is the accusative form of "me". We use it here because the action of picking someone up is a complete, finished action, not a continuous or partial one. When a personal pronoun is the direct object of a completed action, it always takes this special -t ending.

Does the verb hakea always mean "to pick up"?

The basic meaning of hakea is "to fetch" or "to go get". When you are talking about a person or a ride, it is the standard Finnish verb for "picking someone up" from a location.

Why is the ending -sta used in koulusta?

The ending -sta means "from" or "out of" (this is called the elative case). Finnish uses this ending attached directly to the noun to show movement away from the inside of a place. Therefore, koulu (school) becomes koulusta (from school).

Why doesn't the sentence say minun isä (my father)?

You could say minun isäni, but just like in English, if it is completely obvious from the context, Finns will often just say isä (Dad or Father) rather than specifying "my" when talking about their own family members.