Learn Dutch: Het meisje wil de oefening niet doen. - The girl does not want to do the exercise.

This is because of the verb bracket rule. When you use a modal verb like wil (wants to), it takes the normal second position in the sentence. The main action, doen (to do), gets pushed all the way to the end. The rest of the sentence is bracketed in between them!

Why does niet come after de oefening?

In Dutch, the word niet (not) usually comes after a specific object. Because de oefening means the specific exercise, niet goes after it. It also prefers to sit as close to the end of the sentence as possible, stopping just before the final verb (doen).

Since the girl is a third-person subject, why is the verb wil instead of wilt?

The verb willen (to want) is a bit irregular! For most verbs, the he/she/it form adds a -t at the end. But for willen, the correct form for he/she/it is just wil without the -t.

A girl is a female person, so why do we use het meisje instead of de meisje?

While words for people usually take de, the word meisje ends in -je. This ending makes it a diminutive (a word for something small). In Dutch, every single diminutive automatically uses het, even if it refers to a person.