Using the cigarette lighter to power your car amp means that instead of just turning the car on to generate the amp's power, you will need to plug the adaptor into the lighter to turn the power on. You will still need to connect the audio cables in the rear of the stereo, and the speaker will be connected to the amp the same way as well. The only wire that you won't need is the remote lead wire.
Connect the speakers to the amp with the speaker wire, following the manufacturer's installation instructions. Plug the audio cables into the amp's corresponding connections.
Plug the cigarette adaptor into the amp. Lead the audio wires and the cigarette adaptor to the stereo receiver.
Plug the audio cables into their corresponding connections on the rear of the stereo receiver. Plug the cigarette adaptor into the cigarette lighter in the vehicle.
Conceal the audio wires and the wire from the cigarette adaptor under the plastic panels along the floor. This will keep the wires hidden and safe from damage.