How are animals that are hatched from eggs fed by their parents?

Depends on the species. Some, like snakes and crocodiles, hatch as perfect miniature copies of the adults, and have to feed themselves on suitably sized prey pretty much from day one. They never get fed by the parents. Others, like some birds, are fed by their parents for quite some time before managing on their own. Some - like penguin chicks - get fed regurgitated food from their parents gullet/stomach. Others - like owls and eagles get fed scraps of meat that the parents pull from their prey.

Herbivore birds don't get fed as such, but the parents will guide them to places with good eating.