Some people clean their lenses in different ways, but here is how I have done it for decades:
1. If the glass has dust, I use a lens air-bulb and brush to remove it, and never clean it further.
2. I only clean it if the glass has a smudge from my fingertips, water droplets, and such. Before I proceed, I blow-away any dust on the glass first. The next step is to moisten a small area of the lens cloth or tissue with lens-cleaning fluid (never pour this fluid on the lens), and then use this portion of the cloth to wife the lens softly. Right after, I use another but dry section of the cloth or tissue to gently wipe the glass to remove any cleaning fluid residue.
3. If the glass has sand, dust, mud, etc. stuck in place, I make sure that none is left on the glass before I wet-wipe it, because the tissue of cloth will hold the dirt like a sponge and may the glass.
I do use the Lenspen brush when needed to remove dust, and sometimes the cleaning side to remove only very small smudges.