I will agree that you aren't going to save the coil or re-use the wire(why??), but go buy yourself some SSS316L for 3 or 4 bucks; it will come with cotton and is good for a couple years worth of daily vaping. For these coils you can buy a 24 or 26 gauge and experiment, I personally like to buy 28 or 30 and twist two lengths. And the reason I say use Stainless is that it has by far the best taste and can be used in temp or vw mode, just can't pre-burn the coil.
That said, the small end cap on these can be pried off with a couple pairs of small pliers(I used forceps), then the bottom metal plug off the bottom followed by the rubber. Don't damage the rubber piece! I wrap my twisted pair 28 gauge 7 times, 4mm if you have it, but 3.5 will do. This came out to .55 ohms. Leave plenty of wire at both ends of your wraps. Then cut a strip of cotton the same width as the outer shell of the assembly(where the wick and coil go). make a 90 degree bend just past the ends of your coils so both wires point down, and tuck one end of our cotton under the wire leading from what will be the top of your coil, then wrap the cotton around the vertical coil until it is thick enough to be snug when inserted into it's chamber. Bottom wire against the edge and outside of the rubber piece; lower wire thru the middle of the rubber. Snip the wire on the outside of the rubber off flush, this is negative and can(actually must) touch the metal of the casing. For the wire you ran down the middle of the rubber, trim it level with the top of the rubber, then insert the metal 'plug' last. Flip it over and press the upper cap back on and test your work. I really hope that nobody needs this following statement, but there are some people- DO NOT TEST THIS WITH A MECHANICAL MOD!!!! use a regulated mod that shows you resistance and has low resistance protection. Note the resistance, the wire gauge used, and number of wraps for future builds.
If anyone is really interested I could post pics.
Seriously, these things cost about $1.50 apiece, and my first try took about 15 minutes. I am sure the next time it would take about half that. I wrap all my own stuff sso no biggie, but you have to figure in what your time is worth compared to over the counter replacements. I hate 'cartridge coils', but the wife wants simple and enjoys her subtank mini and she had no spares so I ordered her ten and then rebuilt the one she had just because everyone says it is really hard or can't be done. Unfortunately for me she says my build is the best tasting she has ever had so I may be stuck doing them regularly..