Make sure that the flute is balanced properly in your hands. The main points for support are the right hand thumb and the first finger knuckle joint of the left hand. Keep in mind that there is some counterbalance coming from the flute resting on the lip/chin area as well. Orient yourself in a room facing one wall: The left hand palm should face the wall to your right, keeping the elbow joint rather low. The right hand thumb can be placed under the F key, or slightly lower, but oriented underneath the index finger. Make sure that there is no break in the wrist joint, so that the right arm has a smooth line all the way to the elbow. These little adjustments in hand position may encourage smoother finger technique. Fingers move from the knuckle down: the hands don't move. Use a mirror to check your hand position frequently.