How Do I Hand Feed Baby Budgies?

First off, I must tell you that hand feeding a baby budgie is very time consuming and difficult. We only hand feed in dire situations.

If the goal is to raise tame budgies, an excellent way to accomplish that is to let the parents raise them, then take 10 minutes, several times a day, to hold the chicks. Start when their eyes open, about 7 to 10 days. Increase the time as they mature. We have had fantastic results with this method. It really works out well, the exceptions being that you may still end up with an odd personality that will bite (though they are still tame!) But it is my educated guess that these ones would probably have bit no matter how they were raised. Personality plays a definite roll in taming.

If hand feeding becomes necessary due to breeding hardships, read the following excellent article on hand feeding:
Hand-Feeding Implements: Method and Technique by Wanda Barras