Gently apply the brakes when...
Gently apply the brakes when you want to slow down, and release the brakes slowly rather than coming to a sudden standstill. Be similarly gentle when using the throttle, avoiding sudden surges of acceleration or deceleration that can toss your passenger around.
Even a light passenger adds a significant amount of weight high up on the motorcycle, and there are some simple guidelines for her to minimize the effect of her weight. While it's fine for a passenger to move around, she should avoid any sudden movements, especially from side to side. In corners, it's not necessary for her (or you, for that matter) to hang off, but she should lean with the motorcycle and look over your inside shoulder. This will both lessen the effect of her weight on the chassis as well as force her to look up and ahead, reducing the chance of motion sickness or nervousness. It's not necessary for her to maintain a death grip on you or the motorcycle at all times, but she should be constantly paying attention to what's coming up and be ready for a stop or turn.
For your part, you can minimize your passenger's lurching around by being smooth and avoiding sudden changes in braking, acceleration or turning. You can still brake just as hard as you can on your own, but avoid grabbing a handful of brake all at once. Likewise, when you come to a stop, don't stay hard on the brakes right until you're stopped, but rather gradually release the brakes as you approach the stop. In a panic stop you won't have much choice, but under normal conditions this will keep both you and your passenger calm and relaxed. The same applies for acceleration and cornering-avoid being jerky on the throttle or grabbing a big handful at the exit of every corner, and be smooth transitioning from side to side in turns. With some practice you'll quickly find what you can and can't do, and how much your inputs affect the passenger's-and, in turn, the bikes-stability.
The smoother you ride, the...
The smoother you ride, the less your passenger will sway around. That, in turn, means your bike is affected less by your passenger's weight, making it easier to be smooth. This snowball effect makes things much easier for both of you over time, and you will be surprised at how little a passenger can affect your bike's handling.
Over time, you'll realize that an experienced passenger has little effect on the dynamics of your bike and that you can ride in a manner that has her comfortable on the back in practically any situation. A good rider/passenger combination can hustle surprisingly quickly down a canyon road or even around a racetrack-although you shouldn't take that to mean you should be testing your limits with a passenger aboard. Indeed, the consequences of a crash are far greater than if you were solo, and you should be accordingly even more vigilant than usual and well within your comfort zone.
When you are finished with your ride, come to a complete stop with the brakes on and your feet spread wide, and signal your passenger that you are ready for her to hop off. Dismount is just the opposite of getting on: With her left hand on your shoulder and left foot staying on the peg, her right foot will swing over the bike and onto the ground. If everything has gone well you'll both have big grins on your faces and can talk about how much fun you just had.