How do electrons flow in a closed circuit?
There are "loose" electrons in metal conductors (be they traces, wires, plates, etc.)
When you connect a battery to a conductive circuit, the electrons in the battery are being removed from the "positive" terminal and added to the "negative" terminal under an electical potential (pressure) on the inside of the battery. (we'll omit the electrochemical explanation of battery internals here)
The force of the excess electrons pushing circuit electrons away from the negative terminal, and the force of atoms with electrons removed (called "holes") pulling on the circuit electrons causes loose electrons in the conductor to "shuffle" (flow) through the circuit.
Every time an electron "jumps" from the circuit to the "positive" battery terminal, the rest of the loose electrons in the circuit migrate towards that terminal. This "makes room for" an electron from the battery's negative terminal to "jump" into the circuit.