For me, it depends upon the type of surface I am dusting (baseboard/wall vs polished tile/stone vs unfinished wood/raw stone). If it’s a smoother surface - I will just use several microfiber cloths until it is clean. If they surface is more rough, I first “dry mop” with a washable microfiber loose towel or a swiffer duster. Then I use a damp microfiber cloth to clean. I found this system that is amazing for baseboards & walls

Chomp Long Handle Dust Mop:5 Minute CleanWalls Extendable Wall Washer, Ceiling Cleaner and Baseboard Duster - Telescoping Dry Dust / Wet Wash Cleaning Mop with Washable Microfiber Pad https://www.amazon.com/dp/B011RY65WO/ref=cm_sw_r_cp_api_glt_fabc_W3VP38CTMMEDQ1C5K7CN?_encoding=UTF8&psc=1