Make sure you are using the correct size wire before you start your project

First you need the right tools:

-Soldering Iron or Gun (higher wattages work quicker)
-Regular Cigarette Lighter
-Wire stripers
-Solder, a smaller diameter is easier to use
-Adhesive Lined Heat Shrink Tubing

Strip back 3/4″ of the wire insulation on both wires to be connected. Make sure your wire stripers are sharp, you don’t want to stretch the wire when you strip an end off. You also don’t want strippers that cut off wire strands under the insulation.
Cut a 2″ piece of Heat Shrink Tubing, or a length that will be approximately 1″ longer than the solder joint. Choose a diameter of heat shrink that will seal the wire when shrank, most manufacturers list a diameter before and after heating.

Slide the Heat Shrink Tubing over the wire before you connect them! Put the heat shrink over the wires before you solder them together, I can not say this enough. Once they are soldered it would take some voo-doo magic to get the heat shrink on without braking the solder.
SLIDE IT ON!

Now its time to get the wires together. Slide them together by pushing them into each other. Then twist the wires, this interlocks them for the LIFE! Just follow my simple pictures:

This trick will save your fingers and give you a free hand. Brake off a piece of the thiner solder. More or less depending on the wire size you are connecting. The amount to use it a judgment call. Now roll the solder around the wire. This will help lock the wires together before the solder.

Now, touch the soldering gun to the under side of the wire directly on the solder. Always us a flat spot not the tip! The gun will melt the solder immediately touching the tip, this initial molten solder will act as a heat shink heating up the wires quickly. The hot wires will melt the rest of the solder and draw it in..

The time it takes to complete this will depends on the wattage output of the gun you’re using. Remove the soldering gun from the wire as soon as all the solder melts. Now let the soldered joint cool. You just soldered!

Good Job, but you’re not done, it’s time for the Heat Shrink Tubing. This is not the time to get cheap, electrical tape won’t last 6 months!

Cover the solder joint with the Heat shrink evenly.

Get out that lighter, put the crake pipe down, and shrink the tubing. This is where cheep people will fail. Get the adhesive lined heat shrink tubing. The adhesive glue should ooze out the ends and seals the solder joint for life.