Just so you know, I spent an absolutely inordinate amount of time researching this topic.
THE HARD WAY
According to the Internet, these are the best DIY candle wicks. There are other methods for making wicks that take a little less time and slightly less work. But they don't burn as brightly while consuming the same amount of fuel, so ultimately, these are more cost-effective by offering the brightest bang for the buck. The borax and salt solution strengthens the wick and helps it burn brighter and longer while producing less ash and smoke.
Candle Wick Solution
1/4 cup borax
2 tablespoons salt
1.5 cups water
Butcher's twine, cotton yarn, or embroidery floss--just make sure it's 100% cotton
Bring the water to a boil in a small saucepan. Add the borax and salt and stir to dissolve. Place your cut cotton twine or yarn in the solution and soak for a day. After soaking, dry the twine thoroughly. It may take up to three days in a humid area. (I put mine in the dehydrator because I was really impatient.)
After the yarn is completely dry all the way through, melt paraffin wax or old candles, or even cheap crayons, in a double boiler (perhaps an empty, rinsed vegetable can). Dip the strands of cotton lengths for your wicks in the melted wax three times. Dry the wicks on waxed paper or use clothespins to hang from them from a clothesline. You might be tempted, as I was, to skip this step. But for research purposes, I didn't.
If you are using these wicks to make wax candles, you'll also want to reuse aluminum wick tabs from tealight candles or fashion your own from heavy-duty aluminum foil. If you are using these for oil candles, you'll also need a bit of thin wire to hold the wick up out of the oil. Fine gauge crafting wire is ideal (yeah, I don't actually have any lying around, either), paper clips (not so great), or Christmas tree ornament hangers (wish I'd done this before putting all the Christmas stuff away) could all be pressed into service. The tabs and wire holders are not needed if you are making these candles with canning jars and using the spent lid for the support (after you make a hole in it).
Evaluation: These wicks work just fine. They usually light right up and don't appear to smoke or make much ash. But in the interest of full disclosure, I should state that I am not a candle aficionado.
THE "THROW-MONEY-AT-IT" WAY
If you've got the money and would rather buy than DIY, you can get these handy little things called floating wicks. Lydia got me a box of fifty for Christmas, and I finally pulled them out today to give them a whirl. Stick a little wick in the center of the cork-based floating tab (coated with foil on top so that the cork doesn't burn), place it in the oil, and light. And it just lights right up. It doesn't need time to pre-soak in the oil or anything like that. Burns perfectly. They run about seven dollars for a hundred. I got the small ones, and they tipped over sometimes as I was trying to place and light them. After reading the reviews on Amazon, I'd get the larger ones if I ordered again. These floating wicks burn up to ten hours.
Evaluation: I liked them. They're cute and clean, no smoking and no ash. If I had more dollars than sense, I'd definitely just get these. They burned just as brightly as the other wicks.
THE EASY WAY
The easy way is to just get cotton yarn, the heavier stuff like for crocheting washcloths, not the very thin stuff for crocheting tablecloths. Soak it in oil. I swear I cannot tell any difference. I have been using the plain yarn and the yarn soaked in borax and salt, with and without being coated in wax. I'm afraid to write this, scared that I will offend the candle-making gurus. But really, I can't tell any difference. I've been using ten-year-old rancid vegetable oil and current stock (well, close enough) olive oil. I honestly can't detect any difference, even though The Internet Says that olive oil burns cleaner. I'm just sad that I wasted so much time soaking the yarn, drying it, dipping it in wax. For naught. Except that now you don't have to waste your time.
Evaluation: As far as I can tell, plain cotton yarn works just as well, without the muss and fuss. This is what I'm using.
I will add that the soaking in borax and salt and dipping in wax might be important if the wicks are being used to make wax candles. I'm not interested in testing that out, at least not for another year or two. Why? I've got loads of rancid oil and cotton yarn to go with it.
One final, very important note, which nobody mentions online. Maybe because they all have common sense and know this already and figure everyone else does as well. But I didn't. And I was so frustrated because my wicks would work, and then they wouldn't.
So here it is: The wick actually has to be close to the oil. Of course, in my world, it would quite acceptable to have an inch gap between the surface of the oil and the top of the wick, which is supported by the canning jar lid. However, this does not make for a candle wick that burns well on planet Earth. So make sure the base of the wick is pretty close to the oil. Then you can be happy and not frustrated as I was. As the oil burns down, just replace it with more oil, or add in water if you're only putting an inch or so of oil in the jar.
Links to related posts:
Oil Candles
Uses for Rancid Oil
Salt
For further reading:
https://www.wikihow.com/Make-Candle-Wicks
https://candles.lovetoknow.com/Homemade_Candle_Wicks
https://www.redtedart.com/how-to-make-a-candle-wick/