Most bicyclers are quite familiar with changing their brake pads as they're one of the first things that start to go after excessive riding. Over the course of a life though, having to swap out the brake cables can be either hit or miss. The inside of the cables can attract dirt and residue or the cables can get clipped and need replacing. Either way the project is one that can be undertaken in relatively little time and one which also helps get the user more familiar with the workings of their cycle.
Take Apart the Old Brake Cable
The first thing you need to do when replacing a brake cable is to get rid of the old one. There is a pinch bolt located near the brake pad that can be unscrewed to free up the cable from one end. The other end that needs to be removed is near the brake hand lever. There's usually a screw or an adjuster on the outside of the lever that can be unscrewed so the cable can be pulled out. Once both of these devices are free, pull out the old cable and set it aside.
Installing New Cable
Using the old piece of cable that was just removed, lay the new piece of tubing down next to it to get the length and snip the new tube. Place a ferule on the end of the tube and slide a piece of cable through the hole. Leave enough cable sticking out on both ends of the tube so that it can be tightened to both the brake pad and the hand lever. Now reconnect the brake including all the pieces that were removed from the old piece, typically at least consisting of a black rubber casing that separates the brakes and protects dirt from seeping into the cable connection.
Finally tighten all the screws and do the final checks. Make sure the brakes touch and do any final tightening that may be needed. Finally cut the excess cable and tape the ends up if desired. You should now have successfully changed the brake cables in your back in about 1/8 of the time it would have taken to swap out an automobile's brakes...and for a fraction of the price as well.