Unplug the power supplies to the pump switch as well as the sprinkler controller.
Locate the two thinnest wires extending from the pump start relay, and strip 1/2 inch of insulation from the end of both wires using the wire strippers. Use the gauge on the side of the strippers to determine the best slot on the tool with which to strip the wires.
Loosen the master valve and common wire screws in the sprinkler controller with the flat head screwdriver. You can usually find these screws next to black wires and white wires, as well as the markings "P/MV" (Primary/Master Valve) and "C" (Common wire).
Secure the black wire from the pump relay into the "P/MV" slot on the irrigation controller by inserting the stripped portion of the wire underneath the "P/MV" screw and tightening it with the flathead screwdriver. Repeat with the white wire from the pump relay and the "C" screw.
Restore power to the pump and the sprinkler controller by plugging them back in.