how do you connect two copper wires together
With connectors!!! (Wait for an answer from someone who knows more!)
You could try solder. I usually just twist them together and then cover them with electrical tape, although, I guess that's not the proper way.
You have your choice. Some choices depend on the use of the wire. You can solder them, join them with crimp connectors, use wire nuts, or use screw down terminals. If the wire are for electrical house wiring, wire nuts are requires. If for low voltage inside equipement or the like, any of the listed methods will work fine.
