Stray pics (guilde) of me soldering up the Zombie Lights... Note: I'm not the best in the world, but my joints hold. Usually.
1) Strip wire about 1/2-3/4 inch off the end of the wires and place a length of shrink wrap over one of the ends. You'll need at least a 3/16" longer piece than the stripped portion. Moar doesn't hurt (usually). The biggest thing is have enough exposed wire that you can work with it.
2) Twist the wires together so when soldered they will appear as one continuous wire.
3) Solder the wires
I recommend a pencil style for this; the guns tend to get too hot for this kind of work, but if that's what you have, feel free to give it a shot. Melt a little bit of solder onto the end of the tip first, as this promotes heat flow. Then, place the tip on one side of the exposed wires to start heating them up. After a few seconds, apply solder to the wire (not the iron) from the opposite side of the iron. This allows the heat of the wire to melt the solder, not the iron itself and creates a better joint.
4) Slide the shrink over the joint. You should have no exposed metal. If you do, unsolder and get a longer piece of shrink.
5) Apply heat to the shrink wrap to melt it to the wire. A lighter will work, as long as you keep it moving, and a hair dryer on high can work as well. Best is an actual heat gun from the hardware store or one from a craft store.
If you need/want to have three wires coming together, then you twist those together first, then join them to the 3rd wire. The final run will look like a 'Y'
I had these two run together and they were soldered like that to the connector.