There can be multiple reasons for rewiring the stereo in your car. If you've installed new speakers in your car for your current stereo, you'll likely need to connect their wires to the stereo's electrical connector. You might also need to replace the power or ground wires. Soldering is the most common method of a permanent rewiring connection. It is important to connect the wires of the same colour, right down to the colour of the stripes on the wires.
Disconnect the car's negative battery cable as a safety precaution, loosening the clamp for the black cable with a wrench, and removing it from the terminal.
Remove the stereo from the car's dash, prying off all trim panels surrounding the unit with a trim stick, and removing its fasteners with a screwdriver or wrench. This will vary greatly depending on the head unit make and model.
Disconnect the electrical connector from the back of the stereo.
Atach the wires from the connector that are colour-coded with the wires that you intend to connect. Use a pair of wire cutters, and then trim a half-inch of insulation from each wire lead.
Line up the leads of two colour-coordinated wires from the electrical connector and your other device's wiring, and twist the combined leads together
Place the end of a solder spool on the twisted wire leads, and heat it with a soldering iron, making sure the solder touches the wires and not the soldering iron.
Wrap shrink tubing along the connected leads, and apply hot air from a blow dryer or similar heat gun to contract the tubing along the wire.
Reconnect the electrical connector to the stereo, and reinstall the stereo within the dash with its fasteners and trim panels.
Reconnect the battery cable to the car battery.
You can also crimp wires together: Line up the wire leads side-by-side and twist them together so they form a V shape. Then insert a crimping cap onto the connected leads, and clamp the crimping tool onto the cap to close it around the wires.