She forgot to feed the dog.

Literal

She [topic-は] dog [target-に] feed [object-を] give [nominalized-の] [object-を] forgot.

餌をやる is the standard collocation for feeding an animal — note the choice of やる (the rough/casual cousin of あげる) because the recipient is an animal. With あげる, 犬に餌をあげる sounds almost over-polite, as if the dog were the speaker's senior. The structure ~のを忘れる ('forget to do') wraps the whole feeding action in の (a nominalizer) and feeds it to 忘れる as a direct object. The choice between のを忘れる and ことを忘れる is largely stylistic, with の slightly more conversational.