Joining two electrical wires is one of the easiest electrical processes there is. With just a little bit of practice, anyone can connect two wires, and then go on to do more multiple wiring projects based on that experience. Electrical wire comes in two styles: solid copper and twisted copper filament. Both of these types are essentially handled the same way, and it is even possible to merge the two styles if necessary. Of course, due to the inherent risk of electrocution, some people may want to hire a qualified electrician instead of doing it personally.
Disconnect the power to any wires that are hot. Use a voltage detector to insure that all wires are not live before proceeding or there could be serious injury.
Use a wire stripper to remove an inch of the rubber insulation from the ends of each of the wires. Do this by placing the covered wire into the groove for the size wire being used, clamping it tight and pulling evenly toward the end of the wire. This will remove the insulation but leave the wire untouched.
Place the two exposed wires together at their midpoints in the shape of the letter X. Twist the two wires together tightly, and remove any excess by snipping it off with wire cutters. For very thick wire, it may be necessary to use needle-nose pliers to twist the wires together.
Twist an appropriately sized wire nut over the wires and apply pressure while screwing the nut over the wires in the same direction as the initial wire twisting. When the nut seems tight, tug on it slightly to make sure it will not pull free.
Wrap electrical tape around the rim of the wire nut and down the wire to form a full seal over the connections. Make sure that all exposed wire is covered securely. It is better to use too much tape than not enough. The tape will also help hold the nut in place over time.
There are a variety of different size wire nuts available. Some are made for small wire, while others are better for thicker wire. If concerned about working with electricity, consider hiring a professional electrician.
Be absolutely certain that the power is off to any wires you plan to work with.