A budgie parakeet does not attempt to talk until it is about 3 months old. However, the bird is learning during that time, and short phrases should be spoken to it often.
To avoid complications while teaching a budgie to talk, make sure that they are not within hearing or seeing range of another bird while learning to speak. This will increase the chance that they learn human speech.
The best time to teach them is in the evening, using a cloth to cover the cage leaving a visible spot at the door to the cage. This allows the bird to see only you, so he can focus, and reduces his fear. Continue this pattern for several nights so that trust is gained, then slowly start to talk while petting the bird. Use short, simple words such as,"Pretty Joey." This allows the bird to become accustomed to the way that it needs to speak.