How to connect wires
When you retrofit items not originally fitted to your car, you often have to tap into wires or make new connections not already present in the electrical circuitry. The best way to do that is by soldering. Although making nice soldered joints requires a little bit of training and experience, it's still far from rocket science. Practice here doesn't mean months or years, much more like five minutes, especially as we're not speaking about soldering delicate semiconductor components on multilayer printed circuit boards but a couple of thick wires...
You'll need a soldering iron. Not necessarily a fancy one with electronic temperature control, actually, the best one for automotive use feeds on lighter fluid. It is small, lightweight and portable. I have a Weller Portasol but many other manufacturers have similar products. An alternative would be a small, simple soldering iron that can be connected to the battery of the car.
You'll also need a solder. The usual ones come in the form of a wire (made of alloy of tin and lead), with a core containing a non-corrosive flux (this can be clearly seen if you cut it). You won't need any extra flux.
Although, with some practice, it is possible to create perfect soldered joints in one go, the easiest and most reliable way, especially in the beginning, is to use a two step process: first, you coat both wires or parts to be connected with a thin layer of solder (this is called tinning), independently from each other, second, you connect them with more solder.
For practicing, use a length of wire as the one used in the car. Remove 1 cm of the insulation from the end of the wire and twist the copper wires slightly with your fingers to make the individual wire strands stay together. Put the copper wire on the flat surface of the tip of the hot soldering iron and apply the solder from the other side. This is very important, you always have to heat from one side and to apply the solder from the other side. Never heat the solder directly, heat the wire and let the heat transferred by it reach the solder. As soon as this happens, the solder will melt and the appropriate amount will be literally sucked in to fill the gap between the wire strands, fusing them together. The tinning will be perfect when the strands are coated with a thin coat of solder. It's not a problem if some of the wire strands can still be seen under the coat, just make sure the solder forms a smooth, shiny surface. You can always re-heat the wire and add a little bit of extra solder if necessary—but always make sure you re-heat it completely, so that all the solder melts and flows again; never accept new globules of solder glued to the aready existing coating. Everything soldered has to be shiny and smooth on the surface, the solder blending together to form a single entity.
If there is excess solder on the wire or the tip of the iron, simply wipe it off using a damp sponge, and start all over again. Soldering iron stands always have a sponge for this purpose but you can use any similar sponge, however, make sure it is real sponge, not something plastic that will melt on the tip of the hot iron. If you don't have one, you can use several layers of wet kitchen paper towels or a damp lint-free cloth (again, not plastic) but always be careful, the iron is hot.
If you do it the way described, it will be easy and practically automatic. Practice tinning stripped wire ends until you are satisfied with the results.
Now, tin two wires and place them flat against each other so that the stripped, tinned parts will lie flat on each other. Rig something to keep the wire in place so that both your hands will be free (a small vice, a pair of pliers on the table, whatever can keep them temporarily). Position them so that you can apply the hot iron to one side, the flat tip of the iron heating both wires at the same time, and apply the solder from the other side again. As soon as both wires become hot, their solder coating will melt together, using up some new solder as well. As soon as this happens, remove both the iron and the solder and leave the wires cool for a second or so (actually, to get an idea of how long it takes for the solder to harden, you can deliberately try to pull the wires apart during your first attempts).
If you did it right, the solder will form a uniform coating over the wires, shiny, smooth. It should enclose both wires on both sides. If you find that it is nice from the side you applied the solder to but the individual wires can still be seen from the other side because there wasn't enough solder there to fill the gap between the wires completely, try swapping sides, heat the other side now and apply the solder to this side. But swapping sides is only for practicing. In real life, you don't have to solder a joint from both sides, it has to be correct for the first try. In your next attempt, let the heated joint consume a little bit more extra solder. Once you get the amount right, it will evenly fill all sides in one go.
Whenever you have to add solder to a joint, always re-heat the whole joint. Adding solder to one side of the joint so that it forms a piggy-back globule will make a bad joint. The rule of thumb is that, after you are finished with soldering, you shouldn't see any boundary or marks between old and new solder. Everything has to be shiny, smooth, in a single blob of solder. In any other case, the joint will be unreliable both mechanically and electrically.
And again, because this is the single most important issue in soldering, one that makes or breaks a connection: either you tin, make a new connection or repair an existing joint, you always have to heat the wire completely and thoroughly, so that all the solder will melt and flow. The easiest and practically foolprof way to achieve this is to apply heat from one side and solder from the other. This ensures that when the solder side will already be hot enough to melt the solder, everything in between will also be hot enough.
But how to connect them?
When you practice, try connecting the wires at different angles, one parallel or perpendicular to the other. If you make a correctly soldered joint, all of those will be sufficient both electrically and mechanically. But we will suggest a slightly different approach that, in addition to providing a very strong mechnical connection, able to withstand all kinds of stress in a vehicle and, at the same time, will form joints that are easy to insulate and will look as if they were intended to be there.
Strip the insulation in the middle of the original wire and remove the insulation from the connecting wire as well, in double length. Tin the original wire and wind the new wire nicely around the exposed copper. Solder it in place the usual way: heat from one side, apply solder from the other side. As soon as the wrapping wire is evenly covered with solder, you're done. Insulate as you please: if the other end of the original wire can be disconnected temporarily, a shrinkwrap tube is the nicest and most reliable solution.