Learn Polish: To jest biurko nowego pracownika. - This is the new employee's desk.

Polish uses the Genitive case to show possession. Instead of using an apostrophe 's' like in English (the employee's desk), Polish phrasing is more like "the desk of the new employee". Because the owner is a masculine noun, the basic form nowy pracownik changes to its Genitive form, nowego pracownika.

Why isn't the word for desk (biurko) in the Genitive case too?

In Polish, only the owner changes to the Genitive case, not the thing being owned. The desk is just the core of the sentence ("This is a desk"), so biurko stays in its basic dictionary form, which is the Nominative case.

If I want to ask "Whose desk is this?", how do I use the question word "czyj"?

You would ask: Czyje to jest biurko? The question word for "whose" must match the gender of the thing being owned, not the owner. Since biurko is a neuter noun, you use the neuter form czyje instead of the masculine czyj.

Does the owner always have to come after the object they own?

Usually, yes. In Polish, it sounds much more natural to put the possessed thing first, and then the owner. Saying To jest nowego pracownika biurko would sound a bit like "This is of the new employee desk," which is awkward.