Any audiophile will tell you, for the best sound clarity from your sound system, your connections must be soldered together. What they might not say, is how to do that.
Unless your wires are already bare, you will need to strip the plastic casing off of the last half inch of the wire.
With the ends of the wire facing 180 degrees away from each other, twist the wires together so that the copper looks like candy cane stripes. Do not take the ends of the different wires and treat them like a twist tie.
The solder is going to follow the heat. Apply heat to the wire to warm up the connection. Then from the opposite side where the heat is applied, apply the solder to the wires. You may have to briefly apply the solder to the iron to melt it quickly.
Ideally, you want to make sure that the molten solder melts though the strands of the two copper wires, fusing the connection together.
Apply electric tape to your new connection to electrically isolate it. You may consider using shrink wrap, but that would have to be applied before the connection between the two wires is made.
Things You'll Need
Soldering Iron or heat source (there is a conversion for a butane lighter that works well.)
Rosin core solder. For speaker wire, any thickness of solder will do. For electronics, the thinner solder would be better.
Clear and well ventilated space to work in.
Note that you should not use soldering guns. These are very high wattage and generate most of their heat by passing an electrical current through a wire. Because of this, the wire carries a stray voltage that could damage circuits and components. Never use acid core solder, at least for electronics. Acid core solder will corrode component leads, board traces and form conductive paths between components. Remember, the rosin in the solder releases fumes. These fumes are harmful to your eyes and lungs. Therefore, always work in a well ventilated area. Use eye protection at the very minimum of safety equipment. This will come as no surprise, molten solder is very hot. Be careful about the liquid solder splashing you. Your soldering iron (heat source) is also going to be very hot, as well. No playing around with hot tools.