Wire the power jack so that it is tip positive. In other words, the red wire from the 9V battery should be connected to the center pin and the black battery wire should be connected to one of the pin that gets disconnected when the plug is inserted.
Connect another black wire between the unused pin and ground on the circuit board.
Also, connect a red wire from the red power pin to the center pin of your SPST power switch. Connect one last red wire to the terminal that makes connection to the center pin when the switch is toggled to the "On" position.