Newton's third law is one of the most-quoted in physics: for every action, there is an equal and opposite reaction. Lots of times, this is used out of context (to describe politicians, etc.)
The basic stroke in ice skating provides a good example of Isaac's 3rd law in action. When you "stroke" (the basic push in ice skating), you apply a backwards force to the ice. The ice applies an equal, forward force on you, so you go forward. Skaters stroke at an angle, so part of the stroke is wasted. You're pushing forward and to the side. The side push is resisted by the edge of your other blade. The forward push is resisted only by ice/blade friction, so you go forward.
Actually, this is exactly why sailboats go forward, not sideways. The wind pushes the boats forward and to the side. The sideways push is resisted by the long keel, but the forward push is relatively unresisted. Boats are designed to be aerodynamic (actually, "hydrodynamic) to forward motion and are intentionally unhydrodynamic to sideways motion.
Note that these forces apply only to direct pairs of objects. I push on the ice; it pushes on me. As I push in on the wall, it pushes me outward. Third law reactions never involve a third body.
Back to the Physics of Ice Skating
by Karen Knierman and Jane Rigby