Among my private instructors were my father, and as he did not own a motorcycle himself he had to be my passenger. I figured it would be good experience and it was actually quite different from driving alone.
It was not mainly the maneuvering but I felt more obliged to drive safer as any mistake I did would punish someone else too. On a motorcycle even small mistakes can result in a whole lot of pain, so any passenger that is willingly jumping on your bike really trusts you with their life! Either that or they are unaware of the risks.
Other than that the main difference was probably that when you stop at intersections you have to pay attention as the bike then has a higher center of gravity and the total weight is higher, this means keeping the bike balanced is a bit more delicate.
Instructions for the Passenger
The most basic instructions you give your passenger would be to sit close to you, look over your right shoulder if you turn right and your left shoulder if you turn left, to not put their feet down when you stop at an intersection and to be careful not to melt their boots on the hot exhaust pipe. Yes, this has actually happened to us!
Furthermore you can also instruct the passenger to put their hands on the tank if you break really hard, in addition to holding on to your hips with their knees, this way you can avoid to get pushed forwards on the bike by their unsupported weight. If the passenger wants to hold on to you they should keep their hands close to your waist or on your hips as you don’t want to be dragged backwards when you accelerate, imagine what would happen if the passenger was holding on to your shoulders instead!
The last thing to keep in mind is that your passenger should be wearing protective gear comparable to what you are wearing. If an accident does happen I’m sure you would want your passenger to have the same chance to survive as yourself. It could also be the case that your insurance requires your passenger to be protected for it to be valid, like my insurance does!