1 Make sure the wires are clean, no melted insulation.
2 Heat up and wipe the soldering iron tip with a wet sponge to get a clean tip it will sizzle like hell, but you probably never saw the tip so clean. The thin coat of solder on the tip will be clean and shinny.
3 Twist each of the two wires individually to tighten the strands.
4 Use this method when joining wires in a straight run:
If you plan to use shrink wrap insulation, remember to place the tube on the wire now before joining.
Place the two wires together pointing at each other with about half an inch of overlap, interlace the ends together.
Place the clean hot iron tip on the joint, after it heats the wire place some silver bearing rosin core electrical solder
on the wires, it is best if the solder melts from the heat of the wire rather than the heat of the iron. If you melt the solder
toughing the iron with insufficient heat on the wire, you end up with a dull cold joint, rather than a shinny proper bond.
Use very thin solder, not the thick stuff you use to repair water pipes in the basement. If you melt insulation into your joint or
get other foreign material in the joint, start over with a fresh trim of the wire.
Use the lowest heat setting on your iron that will do the job, excessive heat tends to melt insulation and make a mess.
Wrap with electrical tape when finished if you did not opt for the shrink wrap.
p.s. If there is a heat sensitive component near the joint you can use a small alligator clip as a heat sink between the joint and the component.
I also like to use a clean piece of wood as a work surface when making a joint in an odd place, it helps stabilize the wires.
Don't worry it isn't as hard as I make it sound. A little practice will do it