Learn Croatian: Moram ići po sestru na stanicu. - I have to go pick up my sister at the station.

In Croatian, you don't literally "pick up" a person like an object. Instead, you use the phrase ići po (literally "to go for") when you mean you are going somewhere to collect or fetch someone or something.

Why are both sestru and stanicu in the accusative case?

They are both following prepositions that trigger the accusative case in this specific context. The preposition po takes the accusative when it means "to fetch", changing the basic word sestra to sestru. The preposition na takes the accusative when it shows motion toward a destination, changing stanica to stanicu.

The English translation says "my sister", but there is no word for "my" in the Croatian sentence. Why?

In Croatian, it is very common to drop possessive pronouns like moju (my) or svoju (my own) when talking about close family members or body parts, as long as the context makes it completely obvious whose sister it is.

Could I use u stanicu instead of na stanicu?

Typically no. For transit stations (like a bus or train station), Croatian specifically pairs the word stanica with the preposition na. You use na for open surfaces, platforms, and certain public locations, whereas u is generally used when you are going physically inside a fully enclosed building.