てやる

てやる has two uses. It means doing something for someone below you – a child, a younger sibling, a pet – and it declares, roughly, what you are going to do: "I'll show you", "just watch me". Both go on the て-form of the verb.

Doing something for someone

やる is the blunt partner of あげる, so てやる is a blunter てあげる. The one you do it for is your own child, a younger sibling, an animal or a plant. The person who receives takes に, or the thing that belongs to them takes を with の.

Between friends it sounds rough, and about anyone above you it is rude. てあげる is the safe choice for a friend; for someone above you, say what you will do in humble form without any "for".

• × 先生に荷物を持ってやった → 先生の荷物をお持ちしました

"Just you wait"

At the end of a sentence about your own next move, てやる is a challenge or a vow, often against someone who has slighted you. It is rough, emphatic speech: arguments, sports, manga.

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Both uses belong to casual speech. In polite speech the favour becomes てあげます, or is not mentioned at all; てやります keeps the vow sense: つぎ次はかって勝ってやります.