This is how to solder wires properly and then heat shrink them in order to insulate them. Firstly upkeep of the soldering iron is required to keep it from oxidizing. Portable versions of the iron are also available to make work more convenient. A solder sucker is required to suck up and solder left behind by the iron. Alternatively you could use a solder wick which when used with the solder iron can absorb all the solder over the circuit board. Onto the actual process, strip off some of the wire and tie two stripped off ends to each other. Now use the soldering iron to create a strong connection between the wires, once the connection is surrounded by solder put a heat shrink over it. Use a lighter to heat the area that is now covered with the heat shrink now and you are done. This should make quite a strong connection.