I hear all the time from people that I am so brave to take my children out in public. I do take them out with me often to do my usual errands and we go on family outings and to dinner a lot. They are not always perfectly behaved in public, but they really are pretty good. One thing that has helped is to practice the behavior that we expect at home and to be very clear, before we even get out of the car, with our descriptions of how the children should behave. We do this every time we go somewhere. I think it is important for the kids to hear where they are going and why, even if it seems obvious, and to explain exactly what they can expect and how you expect them to behave. Then when misbehavior starts, all it takes is a look, a little reminder, or a gentle pull towards you.
One little thing that helps is to pair buddies together, like they do in preschool, where two kids walk holding hands. I often have each of my three big kids in charge of each of my three littlest kids, then the two in the middle hold hands and walk near me. Also, we do the "ducks in a row" where everyone has their place in line, usually the younger ones in the front with me, then the children walk in order behind. It is very cute, and keeps us from taking up a whole aisle in the store or in a crowd. We even practice the "ducks in a row" at home marching around through the house.
When you are carting eight children around and you have to keep your eye on all of them, you can't have them all going different directions -- I only have two eyes! We often tell the children it is their job to stay with us and to keep their eyes on Mom and Dad.
It all comes down to practice, talk and training, as with anything else. Kids usually don't just know what to do, they have to be taught. Good luck on your next outing!