There are a number of guides out there on rebuilding EVOD coils that could explain how to do it better than what I can provide here. For instance, the videos are the best guide. If you want to rebuild an EVOD coil, try searching on youtube for an instructional.
Assuming you have the right supplies (organic cotton, kanthal wire, ohm tester etc), then you will be able to begin rebuilding it. When I first began to rebuild my coils, I ran into a few problems that even the guides and videos didn't talk about. I'm going to describe them here.
1. Make sure the coil is not touching ANY metal at all. The bottom rubber part needs to be clipped properly, but the coil itself also need to be avoiding any part of the metal sides. This can be frustrating when you first begin rebuilding your coils. So remember to avoid the coil from touching any metal.
2. Instead of rebuilding your coil all the time, you can also just yank out the organic cotton wick and burn the bare coil, then re-insert another cotton wick.
3. I have found a smaller coil to be better, meaning it is wound around a thinner piece of material (nail, hex key etc). This makes for an easier build in general.
4. Buy enough kanthal wire. The wicks or cotton will last a long time, but the kanthal wire can go quick especially when you are first starting since you will waste some trying to get your first coil going.