I forgot something that goes on the equipment list in the previous posting. It's a regular old plain kraft paper bag from the supermarket. Plastic bags won't work, but an empty cardboard box will.
OK, now we have a hand-wound ball of yarn. The tension is probably too tight in some places and too loose in others and it's definitely not a center-pull ball. This is where the ball winder (which I just realized I also forgot to mention earlier, but it's not a requirement, just a nicety) comes in to play. Take this ball of yarn, attach the free end to the ball winder, and drop the ball into the grocery bag on the floor. Another crummy picture, taken of the depths of a paper bag.
The reason for the bag or box is that the ball, if not restrained, will dance all over the floor when it's wound off from the outside (which is why so many of us are so fond of center-pull balls). Frankly, my floors are rarely clean enough that there's nothing for the yarn to collect, mostly because I have a rough-coated collie. I love the collie a lot more than I love spotless floors, but that doesn't mean I ignore reality.
(If I had one, I'd put a good photo of Neil the Collie here. He just turned thirteen, which is pretty old for a collie.)
The next step is to wind off the center-pull ball and then we're ready to make the new skein. Put the swift back into the normal horizontal position and cut some pieces of kitchen twine or slick yarn lengths. These get draped over the swift and the yarn is wound over them. In this photo I've tied the twine into a cute little bow, for some reason, but just draping it works fine.
Tie the end of the yarn onto one of the pieces of twine and start winding the swift, creating a skein. Don't wind too quickly, particularly if the swift is one an inexpensive metal and plastic one like mine. There's a little handle at the center of the swift to use for winding yarn into a skein.
Once there's a reasonable fraction of the ball onto the swift it's time to stop winding and cross the skein ties. They don't have to be tied, just crossed and then draped out of the way. Wind a bunch more on, cross the ties, repeat.
When there's no more yarn to wind, tie the twine off in bows (to make it easy to untie them later). Tie the loose end to one of the pieces of twine so it'll be easy to find. See the loose end hanging down from the twine here? It wasn't quite long enough to reach the next piece of twine, so I just let the extra hang.
Here's the new skein, tied in three places. Why three places? Because my swift has six places where the twine can be put gracefully and I was winding this into a fairly small skein, so I didn't need to use all six places. I thought two ties was too few, six too many, and three about right. Sort of the Goldilocks approach, I suppose.
And here it is twisted back up, with the label attached, ready to go back to my stash. This baby isn't going to tangle again any time soon.
I hope this has been helpful. Most writers don't mention tangled skeins or yarn balls skittering around and collecting dog hair. I can't decide whether this is because they never have such mundane problems or because they don't want to admit to them or because they think no one wants to hear about them.