I stopped reading on the second page so if this has been said, sorry, but it never hurts to say it again.
Cloud chasing is a hobby in itself. The average vaper does not blow those massive clouds and that is probably a good thing. If everyone and their mother was walking around blowing plumes that rival Hiroshima there would undoubtedly already be much heavier regulation than there is.
So, if you decide to cloud chase, chase responsibly. This includes chasing safely and respectfully. People here won't be offended by your clouds, but the masses, including many smokers may be.
DO NOT EVEN WRAP A SINGLE COIL WITHOUT BEING FAMILIAR WITH BATTERY SAFETY
Now, onto the fun part.
Things you'll need: (this is just one method and the method I use, there are other ways, do your research)
Device:
Either a mechanical mod or a regulated mod that will allow you to fire sub-ohm coils (DNA20 or DNA30)
The cheaper route here is the mechanical. When I started out the Smok magneto was recommended as a solid performing cheaper mech mod and it worked for me until I decided to upgrade. It still works just fine.
Atomizer
A rebuildable dripping atomizer is the way to go here. These can be had for as little as 10 bucks or into the hundreds. Watch some videos and read some reviews to find out which type you would like. My favorites right now are the Trident V2 and the Brass Monkee
Wick material
Silica, organic cotton, ekowool, ceramic, stainless steel, bamboo....the list goes on and on here and boils down to personal preference. The 2 most commonly used are silica and cotton with cotton being the cheapest and my personal favorite so far.
Wire
Kanthal is the most commonly used. Most cloud chasers will use the lower gauge wire or twist higher wires together. The lower the gauge the lower the resistance. Watch videos and read up on coil building techniques.
Juice
Juices with a higher VG (vegetable glycerin) content will generally create more vapor. Many cloud chasers actually use zero nicotine juice when they are chasing. I use 6mg juice across the board, but I also don't cloud chase much, I chased until I got a vape that I was happy with.
Tools
ohm meter with a 510 connection (can use a multimeter instead but these are cheap and make life easy), precision screw driver set, drill index, cutters (wire cutters, nail clippers, precision scissors), tweezers, butane torch, a drill, vice grips, and lots of vaper towels
***MOST IMPORTANTLY BATTERIES***
Know what kind of batteries you are using. Know their limits. Know how to find out what your coils are asking your batteries to do and if your batteries are capable of doing it safely. IMHO if you are sub ohming the best batteries currently available are the Sony vtc4, sony vtc5. Also make sure you have a multi meter to check the voltage levels on your batteries before and after charging. If they aren't where they should be, toss em. Batteries are cheap, body parts aren't.