Learn Finnish: Mies unohtaa avaimen paitaan. - The man forgets the key in the shirt.

This is the main point of this lesson! In English, forgetting is a static action (the key stays in the shirt). But in Finnish, the verb unohtaa (to forget) is treated as a movement verb. You are mentally leaving the object into a location. Therefore, it requires the illative case ('into') ending, making it paitaan instead of the inessive ('in') form paidassa.

Why is the word for key written as avaimen and not just avain?

Avaimen is the object of the action. Because the man forgets one whole, specific key, Finnish uses the accusative case, which for a single object usually takes the -n ending. The dictionary word is avain, but its stem for adding endings is avaime-, which gives us avaimen.

How exactly is the ending for paitaan formed?

To form the illative ('into') case for short words ending in a vowel, you simply double the last vowel of the word and add an -n. The word for shirt is paita. We double the final 'a' and add an 'n', giving us paitaan.

I remember that the 't' in paita changes to 'd' in some cases. Why is there still a 't' in paitaan?