Put on your safety goggles. Hot solder is typically a mixture of molten metal and a chemical agent called flux. Make sure it doesn't get in your eyes.
Plug in your soldering iron. Depending on the manufacturer of your soldering iron, it will take 5-10 minutes to heat up.
Turn on the fan and open any windows in the room. Solder fumes can be harmful if your workspace isn't properly ventilated.
Strip the cables with the wire strippers so that bare wire is exposed on both cables.
Lay the cables so that the bare ends you wish to connect overlap.
Twist the bare ends of the cables together.
Apply solder to the tip of your soldering iron. This is called "tinning" the iron and helps with heat transfer.
Wipe any excess solder off on the sponge attached to the base of your soldering iron holder. If your iron does not have a sponge, use a damp paper towel.
Touch the soldering iron to the twisted cables. This will heat the cables so that the solder melts when it touches them.
Touch the solder to the twisted cables. The solder should melt onto the cables.
Slide the heat-shrink tubing over the joined cables so that it covers the soldered point.
Hold the wider part of your soldering iron near the heat-shrink tubing in order to shrink it to fit the cables. If your soldering iron does not produce enough heat to shrink the tubing, use a cigarette lighter.