Wire a new car stereo using a wire harness, along with speaker wire if necessary. Disconnect the ground wire from the car battery before you start work. Wire the speakers first, and then wire the head unit. Connect the amplifier to the power supply and then to the subwoofer. Return the stereo head unit to the dash, reconnect the ground wire, and test the stereo before replacing the dash.
If you are adding new speakers, remove the old speakers, and attach the new ones to the existing connectors. Then, remove the dash, and take out the existing head unit. Connect one end of the wire harness to the car's wiring and the other end to the new head unit. Solder the wires, or crimp them firmly to ensure a good connection.
If you are adding an amplifier, connect its power cable to the car battery. Run the cable through the firewall to the amplifier, taking care to avoid the speaker wire. Run the remote on and RCA signal cables through to the head unit from the amplifier. Connect the amplifier to the speakers and subwoofer, and return the head unit to the dash.
Reconnect the ground cable to the car battery, and test the stereo, checking that every speaker is working properly. If everything is performing well, reattach the dash.