Electrical currents always follow the path of least resistance. They require three conditions in order to flow: a difference in voltage between two points, a conductive path and a closed circuit. When these conditions are met, current flows from the higher voltage point to the lower point.
One example of current flow is completing a circuit with a battery. The positive terminal of a battery has a higher charge of electrons than the negative terminal, and when a wire is attached between the terminals, the current always flows along the wire from the positive to the negative. If the wire is broken or one of the connections is removed from a terminal, the current stops flowing immediately.