so I heat the wire itself and the solder melts onto the wire?
Tin both wires separately before mating the two together.
Get some solder on the tip (of the iron) and touch it to the wire end, grab your solder and touch it to the hot tip and feed it down the length of exposed wire.
After the exposed wire is covered/bonded it is "tinned"
Do that to the other wire.
Grab some heatshrink tubing and cut a section, put it on one wire (below end)
Once they're both tinned all you have to do is put both ends together and apply heat (via soldering iron) and they'll bond as one.
Slide the heatshrink over the joint and apply heat to it and voila!
-Truckin'-