I didn't see this question asked before under the tag audio and after searching [audio] wire harness I was curious to know what are the ways you can securely connect an audio wire harness to a factory wire harness?
From past experience doing installs I've used several methods:
A military splice works well if you want to tap into an existing harness that gives the option to remove down the road. To perform a military splice you would splice into the current electrical system, separate the insulation and use a pointed tool, like a pick tool, to divide the wires and run your new wire in between. After running the new wire in between fold around the divided wired, wrap with electrical tape and use zip ties to secure the connection, example:
An excellent write up, "Military Splice - How to" and picture used from here.
Soldering is typically argued the best way to make a connection between two harnesses. However, a con in this approach is the heat used to melt the solder could burn other wires or wire's insulation leading to electrical issues if the harness being connected cannot be properly isolated. Other than this con all soldered connections should implement either electrical tape or heat shrink tubing:
If you're trying to join two harnesses that are not attached to a vehicle there are stands such as a soldering stand that comes in handy:
Crimping is an option where you insert the wire on either end and use a crimp tool to make the connection. One issue that is typically run into with crimping is the crimp doesn't make a secure connection or the wire falls out if an incorrect connector is used, example connections:
Fold and tape
Stripped wires are folded or wound together and then taped. Not the greatest way to make a connection and connections have been known to come lose. This approach is frowned upon when doing electrical installs but is still an option.