In another of the training segments produced by the National Shooting Sports Foundation, Doug Koenig discusses how to properly shoot with your weak - or non-dominant - hand. He shows how to properly transition the pistol from the holster to your weak hand. If you are shooting a 1911, he says it should have an ambidextrous safety so that the pistol is on safe as you make the transition.
Doug makes the point that you should practice this at home by doing dry fire practice before you do it with live ammo at the range. He notes that after a few transition cycles you will start to get comfortable with it.