How to Solder A Phono Plug to Audio Cable
Choose screened audio cable, and note that phono plugs cannot usually accommodate thick audio cables of more than 4mm outside diameter without butchering the strain relief of the cable shell. The cable retaining claw in the plug is often only good for a smaller diameter of about 2-3mm, so it is best to select screened cable of 2-3mm diameter for most phono plugs.
Before wiring the plug, it is a good idea to insert the metal part into a suitable RCA socket in a clamp, and slide the plug shell and strain relief coil onto the cable first. The temptation to use the socket on a piece of equipment should be resisted. The reason to mate the plug with a socket is that the insulation holding the pin is a soft thermoplastic, and if a lot of heat is needed to tin the center pin this softens and the pin ends up skewed relative to the ground connection, making the plug a bad fit. This can still soften when using the socket, but now the socket will keep the parts concentric.
Problems With the RCA Phono Connector
The main charge leveled against the RCA plug is that unlike nearly all other audio connectors it makes the central signal connector before the shield ground contact. Many a rookie audiophile will have discovered this to their dismay when greeted by a loud buzz as they find the right socket on their amplifier, which obliges by amplifying the AC house current leaking across the transformer winding capacitance and scaring them out of their wits. The buzz goes away when the shield contact mates a split second later establishing a common ground reference.
Phono Connectors are Common so Alternatives to Soldering Cables Up Are Available
Because of its ubiquity, before considering wiring them it is worth considering if the time and effort is worth it compared to getting a pre-made lead. The world is flooded with cheap and nasty Chinese RCA interconnect cables, and if one is needed for an uncritical application like interfacing some computer speakers it is probably best to just buy one.
If a RCA cable is needed for a hi-fi system, however, then it is worth getting something of a known quality or assembling it. Many of the cheaper cables do not even use screened cable, going on the principle it isn't necessary for a 1.5m run at line level signal levels and impedances. While this is true in most cases, it leaves the system open to hum and interference from things like mobile phones.