Many of us would love a talking budgerigar. If you wan to train them to talk you must do so from a very young age and have lots of patience during the training as it can take many months for them to utter their first word. Teach them in short bursts of ten minute lessons and repeat them every few hours throughout the day.
You can start by teaching them their name, say it clearly to them over and over again whenever you see them and speak softly and clearly while doing so. Once they have mastered their name you can move onto other words, it is always best to refrain from introducing new words before they have learnt the previous word. When they get the hang of simple words you can move onto short phrases, you would be surprised that some budgerigars can become quite proficient speakers and are able to utter simple sentences well.
When you teach your budgie to talk, let them perch on your finger and hold them close to your face repeating the word over and over, do not shout, just speak gentle towards the bird and always say the word in the same way. Just like when taming a budgie, only one person should attempt to teach it to talk at first, nobody else should be in the room and the television or radio should be switched off.
Do not give up, budgerigars can become good talkers and provide you with great entertainment, but don't get too disappointed, some budgerigars will not respond and never talk.