I use a damp
Dentek Brush to clean the coil. I also pull the wick out, leaving the coil in place, and dry burn the coil and clean it a little more with the brush. I'll also rinse and let the wick soak in hot water for a while.
My favorite juice, Gourmet Vapors Keoke Coffee, will gunk up a coil pretty quick, so I do this after every tank.