Treneren hjelper barna med øvelsen.

In Norwegian the definite article usually attaches to the end of the noun as a suffix, not as a separate word.
• en trener (a coach) → treneren (the coach)
• et barn (a child) → indefinite plural barn, definite plural barna (the children)
• en øvelse (an exercise) → øvelsen (the exercise)

Most neuter nouns form the definite plural with -ene, but barn is irregular:
• Indefinite singular: et barn
• Indefinite plural: barn
• Definite singular: barnet
• Definite plural: barna

In Treneren hjelper barna med øvelsen:
• barna is the direct object (the ones being helped). “Å hjelpe noen” takes a direct object without a preposition.
• med øvelsen is a prepositional object introduced by med (help with something).

When you help someone with a noun, you use hjelpe noen med noe.
Alternative structures:
• If you want to emphasize the action of doing the exercise, you can use an infinitive:
– Treneren hjelper barna å gjøre øvelsen. (The coach helps the children to do the exercise.)
• You would not use på or til in this context—med is the correct collocation for “help with.”

Yes, but with Norwegian word order and an infinitive marker:
• Hjelpe noen med noe (help someone with something → noun)
• Hjelpe noen å gjøre noe (help someone to do something → verb)
You do not combine both in one clause (i.e., you can’t say hjelpe noen med å gjøre noe unless you mean “help with doing something” as a noun phrase).