Instructions
Repeat the whistle you would like your budgie to learn often, and on a daily basis. Be patient -- It may take several weeks to months for a bird to repeat what you are teaching him or her.
Occasionally whistle slower than you'd like your bird to repeat it. Budgies tend to imitate things a lot faster than we say them, so slowing down will bring a closer result to what you're trying to teach.
Mix up the whistles you are trying to teach your bird often. Eventually your budgie will begin repeating what you are whistling for him, though he will likely incorporate it into his own budgie language and it will have a budgie "accent" to it.
How to Teach Budgies to Whistle
Budgies are not in the top three list of best singing and whistling pet birds, according to BirdChannel.com. However, they are a close runner up. These extremely vocal little birds can mimic lots of different sounds. If you have a male budgie -- females are less likely to learn to imitate you -- listen carefully to it. Many budgies chatter a lot and thus, will likely have an easier time learning how to mimic your whistles.