What is Fleming's Left Hand and Right-Hand Rule?

Did you know that in a magnetic field current-carrying conductor will encounter force? It is called electromagnetic force or emf. All contemporary electric motors and generators are built around this feature. So we know there's a force acting on the current-carrying conductor, but how do we know which way it's pulling? If only a simple procedure could be used in practically every circumstance. Well, Fleming's left-hand rule will do that.