The passenger should hold on to the rider's waist or lower chest. Holding onto the rider's shoulder gives the passenger a lot of leverage and interferes with driver control of the bike. Grab straps running across the center of the seat are probably worst of all. They provide little security, make the passenger wobbly and put the passenger's hands right where the driver needs to sit. On bikes with backrests, especially touring machines with trunks and armrests, the passenger probably won't need to hold on much at all.
Inexperienced passengers are most likely to be frightened when the bike leans over in a corner.
You should address this subject before the ride starts. Most experienced riders just tell passengers to look over their inside shoulder, stay in line with the bike, hold on to them firmly and relax. By looking over the inside shoulder, the passenger moves with the rider and stays in line with the bike's lean. The hold should be firm enough to let the rider know if the passenger is feeling tense and to keep him or her from counterleaning. It should not be tight enough to limit the rider's freedom of movement and control.