There are self-taught engineers have will suggest some electrically unsound connections. I am no expert, but I know how to execute the basic four splices. You need to know them all:
1. Temporary Hook Joint
This joint is made without the aid of solder. It's a temporary joint used in testing or or you feel like living dangerously. Band one wire over another to make the first hook, then repeat the process. To tighten you can gently compress the hooks with pliers.
2. Bell Splice
This is the most common splice you'll see. It's behind every electrical plug in your home. With heavier guage wire such as that case just strip the wires to the same legnth and grip the ends with lineman's pliers and twist them together. For a temporary connection put on a nut, for a permanent connection brush with flux and then solder.
This splice is used to connect a leg to an unbroken lead. First you strip away an area of insulation from the lead. Then twist the new wire around it. With stranded wire there is the temptation to divide the wire into a "Y" and braid it in two directions. This is unwise. The crook of the Y can arc if there is a void and resistance will likely vary between the two sides of the leg.
4. Western Union Splice
This is only for the truly hardcore. (See below) This complicated splice is also called the Lineman's splice. The complicated wrapping pattern actually tightens when pulled which is why you usually see it only with wires under tension. This is probably why it was developed for the telegraph. It's description in the NASA guide describes it as stronger than the unbroken wire. Just note that it is only intended to be used with solid rather than stranded wire.