Step 2: Tin the wire
Dip the end of the wire in flux.
Then stick the wire in something to hold it still. I used a pair of pliers.
Tin the tip of the soldering iron.
Imediately after tinning, hold your iron and solder on opposite sides of the wire. It is important that you hold everything very steady until the solder begins to flow. As soon as solder flows, quickly move the solder and iron out to the end of the wire. This should quickly coat all the metal with a thin layer of solder.
In a perfect world, Terry (my soldering overseer) says the iron should touch the wire a fraction of a second before the solder does. And of course, remove the solder a fraction of a second before removing the iron.
Move too slow and you get melted insulation, which doesn't actually hurt anything, but wouldn't pass a NASA inspection apparently. You could also get large globs of solder on the wire.