Doc here,

imp:
Mine is similar to Mike's..
For most small jobs, use a 40 watt Controlled station OR pencil Iron.
About a pound of 24 Ga , 60/40 Rosin Core solder.
Strip Each wire Approx, 1 1/2 inches back.
Slide Shrink tube (approx 3 inches) over the wire, and another approx 1/4 inch smaller , and different color, with the black tubing. Twist the ends around the center of the wire at about 1 1/2 inches of the bare wire, one clockwise, one Counter Clockwise.. Trim ends.
Give the wire the "Tug" test for good mechanical fit.
Heat your wire and Solder From the Center out ALL at the same time, until the solder flows, and "Wick it toward the ends of the wires.
Your joint should be Clean smooth and SILVER, not gray, (gray is a "cold joint", if you get this cut out the section and start over.) Trim excess Whiskers.
Slide the shrink over the joint and heat to fit. Slide the second over the first and shrink. If you use a different color tubing on the second you can use it for "color coding" ) Black/Red tubing = 12 volt ect...
IF you use 60/40 Rosin core Solder, there should be no need for added Rosin on MOST small jobs.
Doc

imp: