"Shake out the hand, and turn it over. Nestle the violin between the thumb and index finger. Place into playing position. Make sure you still have the gap here, and practise 4th finger pizzicato."
Shake out your left hand into playing position and bring the violin to your hand. This helps prevent the hand from distorting.
Support the violin with your right hand to encourage a calm left shoulder with your left elbow able to swing freely under the instrument. Notice how the left thumb moves with the hand when crossing between E and G-strings for the pizzicato.
How deep the violin sits in the hand depends on the size of your hand, however the violin should not touch the bottom of the V-shape made between thumb and fingers. Keep a space here.
Every hand is slightly different, especially the length of thumb and fingers. Players with smaller hands can let the violin sit lower in the hand so that they can reach the fingerboard more easily, while those with bigger hands and/or longer fingers can let the violin sit higher in the V-shape.
Placing the thumb very low so that it can't be seen is not good as this can prevent the thumb from being free. The thumb should be as free to move as possible....