Keep in mind that hockey is a game played on a frictionless surface, and that the puck, as well as the players, are in constant motion. Players will try to muscle their opponent out of the way for a shot on a goal or to clear the pressure off their goaltender by shooting the puck down the ice.
Hockey is a territorial game much like football.
One way to tell if a team controls the neutral zone is to watch which teams' players can carry the puck through it. Watch the benches periodically for line changes. Defensive breakdowns result, and many times this will lead to an excellent scoring chance for the other team. Watch the time clock when a player is in the penalty box. Sometimes teams use this opportunity to execute a breakaway.