A parrot does not realize he is biting too hard until he gets a response from a human, or even another pet, a dog, a cat, etc. The most effective reactions, will, naturally, depend on your individual bird.
If you have a young parrot, one who has not had much human interaction, you can teach the bird what is acceptable by gently distracting him with a tickle or a toy every time his beak gets too nippy. Ignoring biting behavior works in some cases, although usually only when the bird is trying to get attention. Alternatively, you can say a loud clear, “No bite” or similar phrase and move your hand or finger quickly away.
If you decide to ignore your feathered friend, watch out for his displeasure. Mine have a habit of getting fed up with being ignored (actually what they perceive as being ignored), or maybe it is just that they feel one of their flockmates is getting more attention than they are. They will light on my shoulder and give me a smart nip on the ear – sometimes bringing blood.