How do I proceed with taming my budgies?

Severe punishment is the way to tame the savage parakeet. Whips and harnesses and an electric prod will come in handy. Be merciless. Raw power is the only thing that can gain their respect.
If that fails, just bribe them with treats and speak softly. Also repetition. try to get them to sit on your finger many times during the day, eventually they'll get used to you handling them.