I'm afraid, I don't have any great insights for you. Relax, don't worry, and keep shooting.
The techniques differ little when using the 70-200mm than with using the 80-400mm. You need to give VR time to work by pressing the shutter halfway, and if for some odd reason you are using a built-in flash with this lens, you need to wait for it to recharge as well. Unlike the 80-400mm VR, the 70-200mm VR-II has an active/normal mode switch. I follow the manual's suggestions on which to use; perhaps others can provide more specific examples of when they use Active mode.
Handholding technique still counts, and you should guard against the effects of fatigue when shooting for an extended period of time. Use the lens hood whenever possible. Choose your aperture based on the shutter speed you need and the depth of field you want. While like most lenses, the 70-200mm VR is optically best at middle apertures, especially handheld I wouldn't sweat the differences. Even with VR, when shooting outdoor sports I prefer to use a monopod.
If you want to photograph a man spinning, give some thought to why he spins. Understanding for a photographer is as important as the equipment he uses. - Margaret Bourke-White