According to Newton's third law ,action and reaction are equal and opposite to each other. But there is a very important point that these so called action and reaction forces are acting on different bodies. A net force can be calculated from forces acting on the same system. When there are two equal and opposite forces acting on the same system, the resultant force is definitely zero and the system will not accelerate.
Eg:While skating, our shoes exerts a force on the ground in the backward direction whereas the ground pushes back in the forward direction. The action Force is acting on the ground and the reaction force is acting on the shoes ie two different objects and hence we move.