Learn Turkish: Yarın kütüphanede çalışıyorum. - I am working at the library tomorrow.

Just like in English (I am working tomorrow), Turkish often uses the present continuous tense (-ıyor) to talk about fixed plans in the near future. The word yarın makes it clear that this is a future plan, not something happening right now.

Does çalışıyorum mean I am working or I am studying?

It can mean both! The verb çalışmak is used for both doing a job and doing schoolwork. You usually tell which one it means from the context. Here, studying or working at the library both make perfect sense.

What does the -de at the end of kütüphanede do?

It is the locative case suffix, which translates to in, at, or on. Kütüphane means library, and adding -de makes it kütüphanede, meaning at the library.

Why is the present continuous suffix -ıyor instead of -iyor here?

The suffix changes based on vowel harmony to match the last vowel of the verb root. The verb root is çalış. Because its last vowel is ı, the suffix must also use an ı, making it -ıyorum.