The official way to use it, if I remember the package instructions is something like this:
Use the brush end to flick large particles off the lens surface. I usually use canned air for this purpose, if available.
Then use the carbon pad end to remove any areas of grease / dirt. Usually the entire lens surface is not covered with grime, so consider this to be more for spot cleaning. You clean the pad surface by putting the cap on, and rotating the cap. The dirt and contaminants are supposed to drop off with the carbon particles, while you recharge the surface with new carbon particles. I find the concave surface of the carbon pad to be a good fit to some very convex lens surfaces. An example would be the rear surface of the Zeiss ZM 21mm f/2.8 Biogon.
If there is a large surface to be cleaned, then it would be prudent to use lens cleaning fluid and lens paper first to degrease the area.
The carbon seems to be effective at removing grease and small stuck on gunk. It also acts as a black "filler" for small scratches to make them less noticeable. If the carbon particles bothers you, then you can always use canned air to blow them off.