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• PVC tape is the simplest and easiest but not necessarily the neatest. NEVER simply bind up a cracked mains lead with PVC tape.
• Heat shrink sleeving is an excellent method. It comes in a variety of sizes and colours, pre-cut or in a continuous length. Choose a size which is no more than twice the diameter of the joint you need to insulate, and don't forget to slip it onto one of the wires before you join them! If soldering, keep it away from the iron. Once you're ready, slip it over the join and heat with a heat gun until it has fully shrunken. If you don't have a heat gun to hand, you can hold it very close above a soldering iron and it should shrink slowly, but be very careful not to let it touch the iron.
• Sugru can be used to insulate a join as described above, such as in a headphone lead, but don't rely on it alone to provide strain relief. If you need strain relief then one solution would be to knot the lead either side of the join to give the Sugru something to hold onto.
• The earth wire in the type of mains cables designed for permanent installation is often uninsulated. Green and yellow striped sleeving is available to slip over this within a mains socket or wall switch to prevent it touching a live connection. This will sometimes be useful in other circumstances, but avoid using it where might confuse the next repairer into thinking it's an earth wire when it isn't.