Switch off the main power to the house and disconnect the generator from the transfer switch.
Feed one end of the 3-wire plus ground cable into the output area of your transfer switch. Depending on the amperage your subpanel will draw you will need between 6 and 10 gauge wire. For 30 amps use 10 gauge wire, 40 amps use 8 gauge wire and for 50 amps and above use 6 gauge wire.
Cut the outer sheath off the cable and separate the individual wires. Strip the last half-inch of insulation from all the constituent wires.
Twist the green wire from the cable to the green wire coming into the transfer switch. This is the ground and it should bypass the switch. Secure the splice with a wire nut. Repeat for the white, common wire.
Insert the bare metal of the red wire into the top terminal on the switch and tighten the screw down hard. Repeat for the black wire on the bottom terminal of the switch.
Feed the opposite end of the cable into the subpanel input hole. Cut the cable so that you have enough wire to lead connect to the main terminals at the top of the panel and to the bus bars for the neutral and ground.
Remove the outer sheath of the cable and strip off the last half-inch of insulation from each wire. Connect the green ground wire to the ground bus bar and the white wire to the neutral bus bar. Tighten the screws firmly. Note that in a subpanel installation the ground and neutral bus bars should be isolated.
Insert the red wire into either the top or the right main terminal. Insert the black wire into the remaining main terminal. Tighten the terminal screws firmly.