Filare / Reeling
Reels throughout the world and history have had different appearances, but their main function is to allow the cocoon to be unreeled efficiently while keeping the thread organized.
You can get fancy, but a ball winder works fine.
First, this is only how I do it, and certainly not the only way to reel silk. I prefer my method because it doesn't require anything expensive, and so is more useful to beginners. But most importantly, it works!
I'm also more particular than others in pulling off the waste silk and finding the filament ends on my cocoons. Some people swish a chopstick about in the water, and take what they get.
Bend the wire into a thread guide - there's a picture of mine a little further down. It pokes out from the side of the pot over the water, where there's a larger horizontal loop about 2" across, then a straight portion up, and a smaller, vertical loop about 1/2" across. Mine clamps to my pot, but I expect you could bend the other end into a loop to fit over your pot handle. Your cocoon filaments will be loosely gathered together by the larger loop, travel upward, and join together into a single thread as they pass through the top loop. Make sure your wire bends in a way that you can thread your filament through the loops without having to let go of the thread end.
Fill two large pots with water - wider is better so the cocoons aren't crowded up out of the water (they float) and so they can move around freely. Put your cocoons into one pot of water and heat them (below simmering) for 30-45 minutes. I like to hold them under water with chopsticks and watch the bubbles come up. The water will get yellowish with the softened sericin.
Heat the second pot of water to a similar temperature and attach your thread guide to it. When the cocoons are ready, remove one cocoon and pull off the outer floss. (Careful, they're hot!) Doing this over a dark background will help you see what's happening. Pull off any filaments that stick out. You're only losing the part that will give you a headache later. There's still plenty of silk left on your cocoon. Eventually you'll notice that you're down to one strand, and the cocoon can be dropped by it like a yo-yo that doesn't come back up.
Drop the cocoon into the second pot of hot water, thread the silk filament up through the guide, and secure the filament end. I used to try to stick the single filament to a piece of tape, but now I just leave it attached to the waste silk. The waste keeps the end from floating away and I drop it into an empty bowl to keep it contained.
If it's very quiet, you can hear the silk pull from the cocoon. If it makes a crisp ticking sound, the sericin hasn't been softened enough and you're likely to have it break during reeling (or you'll think you've found the One True Filament when in fact you're still on the broken outer layer of waste silk.) I've found that a soft whispering sound is about right. It IS possible to have them too soft, which causes goopy lumps to reel off the cocoon.
Repeat this with each cocoon until all the outer waste has been pulled off, and all the filaments have been found and threaded through the wire guide.
Remove the center plastic core from the ball winder and fit a TP tube into the space instead. Tape it to the base with tabs of masking tape. Because the wet silk will compress the cardboard tube quite a bit, it helps to NOT have the plastic core in the middle - otherwise it's very hard (impossible?) to remove the tube from the core of the ball winder.
Gather together the filament ends and break off the waste if it's still attached. Tie the filaments to the TP tube on the ball winder and begin reeling.
It's not strictly necessary, but it doesn't hurt to reel over a distance to allow the silk time to dry some. If I have the space to do this, I clamp my lazy-kate as far away from my pot as I can get, and take the silk around a bobbin on it and back to my pot where I have my ball winder (and I can watch the pot while reeling.) By going around a bobbin on a lazy-kate, the silk doesn't drag and stick - the bobbin turns freely. Improvise with anything that spins. Even a sewing machine bobbin on a wire would work if you wanted to do this.
I like to keep an eye on the pot for any cocoons that have dropped out. They tend to stop bobbing in the water, and drift off toward the edges of the pot - another good reason for using a large pot. Pull them out, re-grope the end, and wind it around your thread as it passes over the top loop, snapping off any extra. The sericin will glue it to the main thread.
As you reel, you'll eventually notice that the cocoons in the pot become transparent, and the thread between your fingers feels finer than at the start. This is a good time to stop. You can reel endlessly if you continue to add in new filaments as the old ones run out, but I find that the length of silk provided by one batch of cocoons is plenty enough to work with at one time.
Winding, or re-reeling:
Later in the day, when the silk has had time to dry some, I put the tube onto my lazy kate and use the ball winder to re-reel it onto a fresh TP tube. A little distance helps it to dry, but the important part is to loosen any areas where the silk might be sticking to itself. Re-reeling also bring the inside silk to the outside where it has a chance to dry better.
Twisting and Throwing:
I save up tubes of reeled silk like this until I'm ready to twist. How many you combine, and in what way depends on the thread you want to make. Right now, I prefer to take two reelings of about 25 cocoons each, and hold them parallel while using my spinning wheel to insert twist. This is equivalent to a single thread of 50 filaments, twisted.
Then I take two groups twisted that way, hold them parallel and twist them in the opposite direction (called throwing, making a z/s 2-ply silk thread of about 100 filaments total. If you like thicker thread try twisting three or more reelings before throwing.
To make the thread soft and white, the sericin needs to be removed by boiling the thread in a solution of soap and water.
Usually, I like to be able to do my craft and look medieval while doing it. This certainly doesn't fit the bill! But honestly, reeling and throwing was a huge industry early on, and was done with water powered machinery. There's just no way I can duplicate that on a small, home scale. So in this case, I settle for the product if not the process.