When wakeboarding, after you have done your deepwater start, you'll hold the tow handle parallel to the water with palms down and knuckles pointed up. Keep the handle low and on close to your lead hip. See the photo for illustration on the right side of this page.
When slalom waterskiing, after you have done your deepwater start, you'll want to hold the handle perpendicular to the water. Your grip will be hand over hand. The reason for this grip is so the handle will be in position for when you let go of the handle to stretch around the buoys and then re-grip the handle as you set yourself up to round the next buoy. Click the photo on the right side of this page to view this type of grip.