It's usually best to get one bird at a time so you have a chance to tame each one individually.
At this point you just want the bird to stop being frightened of you. Petting and cuddling may
come later once the bird settles down and learns to trust you. Right now you just want the bird
tame enough to sit on your finger or shoulder without feeling threatened. Stick training can
usually accomplish this. Take two long perches (one in each hand) and hold them at one end.
Put the other end slowly in front of the budgie and press against it's chest. As you do this,
firmly and clearly say "up!" Once the bird has stepped up try it again with the other stick.
Do this for a while (training
sessions should only last 15 minutes at the most) and try to end on a positive note. At first
the bird may fly off the perch but eventually it should stay on. Try to do it in the bathroom
or some other place where the bird can be quickly retrieved without trying to dig it out from
under furniture. The next session if your bird is doing well slide your hand a bit closer up
the perch. Keep doing this in every session until you can get the bird to step onto your finger
while it is parallel to the perch. Soon it be willing to step up on your finger instead. Pace
each step according to how well the bird is doing. If it becomes very frightened at your finger
being so close pull it back a bit. The object is to accustom the bird to your hands. Remember
to always use the "up" command while training (I never use it once a bird is tame though).
These sessions should slowly aleviate your birds' fear.
A few other tips:
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