Audio cables are prone to breakage from daily use --- especially at the phono plug. The insides of an audio cable are made of metal (mostly copper), so every time you roll, twist or step on an audio cable this amounts to bending a piece of metal --- and there is only so many times you can bend a piece of metal before it breaks. Replacing a stereo phono plug is similar to replacing a mono phono plug, but it requires dealing with only one extra wire. The stereo phono plug has three visible connectors that you would insert into a stereo jack; these are the tip, the ring (just below the tip) and the sleeve (the biggest connector just below the ring). A mono plug, in contrast, only has a tip and a sleeve.
Unscrew the casing of the dysfunctional plug by hand or cut it away with a utility knife.
Examine the wire connections and make a note to their configuration.
Cut the cable with the wire cutters near the old stereo phono plug.
Strip approximately 1 inch of the outer insulation from the cable.
Twist the metal (usually copper) shielding into a wire.
Strip approximately 1/4 inch of the insulation of the two inner wires.
Unscrew or disconnect the casing of the replacement stereo phono plug.
Feed the audio cable through the casing and insulation tube if it has an insulation tube.
Solder the shielding wire to the metal prong corresponding to the sleeve of the replacement plug using the soldering iron and solder.
Solder the other two wires to their corresponding metal prongs.
Fit the insulation tube around the connections, if necessary, and screw or connect the casing in place.