Cockatiels can mimic human speech the same way they mimic the calls of other birds in the wild. Repeating a phrase or sound over the course of weeks to months will train the bird to "talk," or attempt to recreate the sounds that it hears. The average cockatiel can be trained to mimic sounds in about four weeks.
Talk to to the bird constantly, and repeat the word that you want the cockatiel to learn. The bird will gain trust and comfort with the owner and is more apt to learn. Reward the bird when it repeats the word to speed up the learning process. Continued rewards will also keep the cockatiel's attention.2
Speak the sound or phrase into a voice recorder, and then play the recording back in a loop. As with intensive personal interaction, this is a very effective method to get the bird to talk. Hearing repetitive words nonstop can have the bird repeating them within days, especially if it is an adolescent. The word or phrase should be short and not contain the 'S' sound; cockatiels have trouble, as do most birds, with repeating the 'S' sound.3
Place the cockatiel in an environment where the sound or phrase is repeated often. If the bird is taken to an office where people are answering phones, for instance, it will surely mimic the greeting that it hears repeatedly in a workday. Many environments have similar repetitive sounds that the bird can learn, given adequate exposure.