The instrument needs to be stabilized. This is a hard concept, but the violin should never be allowed to slide, or to twist, or sink towards the floor, etc. If this happens, you will squeeze with the left hand, which freezes the fingers, destroys intonation. Squeeze is a response to instability. If the instrument is supported from the jaw, collarbone, and shoulder, it will not shift. First, lay the violin on the collarbone, then place the jaw on the chin rest as if you were laying your head on a soft pillow and not trying to pin it to the bed. The aim is for contact, not for pressure. Pressure prevents movement of the head.
Take the left hand away and the violin should not move. If it does, adjust the angle or place it further back or further forward on your shoulder. Most people place it too far forward on the shoulder, near the arm. This makes the shoulder hump up. Let the shoulder go back and let the instrument stick out. This gets rid of some tension before you even play a note.
If your head is bent down to the point where you force the head against the chin rest, you are probably humping the shoulder up, squeezing the back of the neck, and limiting the motion of the arm. You will get tired and the tone will be terrible. If your head is resting so that its weight supports it diagonally, you will feel better. If you feel strain in the neck after one or two minutes, stop. Start over. It is better to stop than to strain. Don’t strain to get support.
Take a few minutes each day and hold the violin without the bow, and practice breathing. Then hold the violin and play some open strings. Let the left hand hang. This way you can practice support without having to worry about placing the fingers. After a few minutes, place some fingers down and see if you can keep the instrument supported without clamping it with the left hand.
If you start to feel tension in the left hand or arm, stop. Shake your arms out and start over. Support is gained by repetition of the correct motion, not by endurance of strain. When you can support the violin correctly, the left hand will be free to move, shifts will feel easy, and the tone will be fuller. You will start to feel like the violin is not something you are holding, but something that is just sitting there.