Motorcycles are great!

Tori picked up on one of the most important things new riders can keep in mind.

If you're on the back, don't lean against the turn, lean into the turn. Bikes use centrifugal force to travel upright and to not fall over in corners. The idea is demonstrated here, and then it's also demonstrated here. Totally cool.

It also helps use that momentum/force to travel through the corners. Since the gyroscopic effect makes the spinning wheels want to stay upright, changing the angle of that momentum carries you in the direction of the angle. Angular momentum is just a manifestation of linear momentum.

This is balanced against the centripetal force of the tires helping the bike maintain that curved path against the centrifugal force trying to pull the bike straight.

Also, try your best not to focus on one point in the road while in the turn. Your eyes will follow it, which means as you get closer you'll lean further over. Eventually, you've leaned too far over, also throwing off the balance of the bike.

It's much more simple than it sounds, and a rider should/usually will give a quick run down of what to do if you've never been on a bike before.

Basically just relax, don't find leaning into the corners because you won't fall over, and look through the corners. Then enjoy the ride.