I was right where you are a few weeks ago. This is my suggestion from many hours of trial and error. I have an AC9 which has a 3.5mm wick hole, so I'm not sure the size of the wick hole on the ZAP.
Cut a piece of mesh.. let's try 45mm by 60mm. Cut all strands off. Wash in warm water and some dish soap to get any machine oil off, then blot dry with a paper towel. Take out your torch and give it a nice even burn so it's brown. If your mesh is curling, just hold both ends and slide it back and forth against a table edge or something similar.
Now, get one end and while working it back and forth, roll it as small as possible. You're going to want to roll this solid and as tight as possible. At the opposite end of the mesh, fold it over to create a crease, which will give you a solid, strand free edge. Keep rolling it until your fingers bleed. you want to roll it as tight as possible, and when inserting into the wick hole, you want some extra room. Not too loose so it's hard to cram in, and not too tight where it will fall all the way down and instantly touch the bottom.
If all goes well, hold one end with some tweezers, then torch it for about 2 minutes. Let it cool, flip it, then torch again for another 2 minutes. Put some juice on the wick until it's soaked, then light it on fire and let it burn down. Do this 2 more times.
Put the wick in, secure the ground, then start to wrap your coil. Take the ZAP off your ProVari and hold the wire while turning the ZAP, making sure that your coil is touching the wick with each wrap. When securing your positive connection, keep the lead as short as you can get it from post to wick. Use a small flathead screwdriver or something similar and even out your coil. Turn your ProVari down to 3.3V and dry burn until all the coils glow evenly.
You want the coils to start to glow from the INSIDE-OUT. If you notice the top coil is glowing brighter than the rest, keep adjusting them. If you adjust the coil while it's glowing, it will be a lot easier. Once everything is glowing well, add a few drops to the coil and bring your voltage up a bit. Burn off the juice and look at the coils (preferably in a dimly lit room). If the juice is vaporizing and you don't see any coils glowing, you're probably good. Do this a few more times and increase the voltage to your desired level. If you dont see any coils glowing while it's vaporizing, then you are good.
Fill your tank and vape away.
Hope this helps! Once you are good with the process, you can start experimenting with other wick types and coils. I just find it easiest to start out with a solid wick because the wick won't shift much and you can wrap a coil that will stay put and have a harder time developing hot spots.