Holding the bow correctly will insure the greatest possible ease in playing a smooth and even sound. It will aid in achieving smooth bow changes, dynamics, legato, staccato and much more in the violin learning process. This video is even good for more advanced players that need to better their technique.
Make sure that you lift your arm just enough when playing on the G-string in order not to get problems with your wrist. Use your elbow and not the shoulder. Try to be as relaxed as possible by only applying pressure with a twist instead of muscle.