Riding two up is a lot more of a task than just putting someone on the back of the bike and riding off as you normally would. There are several considerations you need to keep in mind while riding two up (with a passenger).
The first thing that becomes obvious immediately as you take off from a standing start is the acceleration of the bike is decreased. Keep this in your mind at all times. You will not be able to just gun it and gain speed like you could when you were alone and adjust your riding style accordingly. The on ramp is a place where this becomes obvious.
So when you pull out of the parking lot onto the surface street give yourself a lot more space. You will not be able to accelerate as fast as you could before putting the passenger onboard.
The second thing that becomes obvious is braking. It is amazing how much more brake is needed to stop with a passenger. My hope is you are reading this before you are discovering it on your own. You have to adjust your following position when riding with a passenger as your stopping distance has increased. Keep this in your mind at all times!
Next is turning. Pay attention to those turn speed signs when riding with a passenger, this is a time they are referring to you. Though you are able to complete a turn t the same trajectory and speed you are able to make it alone your ability to make a maneuver within the turn is decreased. This usually is of no effect on the highways but it comes into effect on the two lanes.
Wind will affect you greater when you are carrying a passenger. You will need to adjust your lane position to compensate for the wind, both the natural winds and the turbulence coming off other vehicles on the highway.
Even with all these considerations riding with a passenger is a wonderful experience.
I have a fixed set of hand signals I use when riding with a passenger.
With the exception of getting on or off the bike I tend to let my passenger guide the trip as other than being in a side car there is no more helpless situation a person can find themselves in than being a passenger. So I become more of a horse when riding with a passenger and have developed these signals to help them guide me.
Safe to get on or off the bike is a strong head nod. (I give the head nod)
Make a left or get into the left lane. Advise the passenger to pat you on your left side. If you are already in the left lane take the next exit otherwise change one lane to the left when it is safe to do so. The same holds true for a right or a change to the right lane with the signal being a pat on the right side.
If the passenger needs me to stop they will pull back slightly on both of my sides.
Do you want to take this exit? I will point at the exit sign and then give thumbs up sign. The passenger will respond with either thumbs up or grabbing both of my sides and pulling slightly back, or even a pat on the side that the exit is on.
If I need gas I will point at the gas sign that is prior to the exit on the highway and give a thumbs up for a longer duration. Even if they do not want to stop at this time there is nothing they can do about it. I need Gas.
If I want to ask if they are doing ok I will pat them lightly on their left leg. They reply with a light pat on both sides.
A light pat on both sides means go straight or just go. What I tried to do was mimic the input a horse receives through the reins.
When they clunk their helmet against mine like in a shift, I will rub the back of my helmet like it was my head they hit.
Hope this helps, I am sure I can think of more.
Ride Safe
Glen