Back when i used tanks i used to take a lot of time soaking and cleaning my coils. I never recommend dry burning the coils because you can melt the rubber grommet in the base and that taste just never goes away. It was alot easier to just buy a 5 pack of coils for a couple bucks (they are so cheap now a days) and replace the coil every week.
But if you must clean. Some use rubbing alcohol, thats sketchy and you should definitely rinse it EXTREMELY well because isopropyl does leave behind a residue. I would just hold the coil assembly with a pair of pliers and let my sink blast it with hot water. This was before i realized it was just easier to buy a 5 pack of coils which lasts 1+ months.
Learning to build your own coils and drip is the best way. But thats another story all together!
-Crit