When attempting to vibrate for the first time or when relearning vibrato the right way, start on the E string with the 1st or 2nd finger until you feel secure.
Apply the fingertip to the fingerboard without pressing too hard and keep your finger round and errect. Apply more pressure on the left side of your finger tips.
Pull back with your hold hand and arm keeping your wrist straight (arm vibrato) so that the finger joints straighten out somewhat.
Bring your hand and arm back to the original position.
Do this repetitively until you feel that the motion is becoming natural and pick up the tempo progressively. Try to have a smooth, even, and consistent motion.
When you have mastered the vibrato on the 1st and 2nd fingers add the 3rd and 4th but don’t switch strings until you feel comfortable with your motion.
The lower the string the harder it becomes to vibrate because of the angle of your fingers. Keep your arm under the violin and not too much to the left. This will bring your fingers closer to the strings.