Learn Hardcore Norwegian: Barnet hjelper piken.

Barn is the base noun, meaning child. In Norwegian, the definite article is usually attached to the end of the noun, so barnet means the child.

A useful pattern is:

et barn = a child
barnet = the child

Also, barn is a neuter noun, which is why the definite ending is -et.

Why is it piken and not pike?

Because piken is the definite form: the girl. The base form pike means girl, while piken means the girl.

So:

en pike = a girl
piken = the girl

As with barnet, Norwegian usually adds definiteness to the end of the noun instead of using a separate word like English the.

Why is there no separate word for the in the sentence?

Norwegian often uses a suffix for definiteness instead of a separate article before the noun.

So in this sentence:

barnet already means the child
piken already means the girl

That is why you do not need a separate word equivalent to English the.

What form of the verb is ?