first you wipe of the worst grime with one of those squeegees that has a sponge on the back side. try to catch dribble with old cloth or so. (some will spill if you’re not a super pro. wipe it off the floor later.)

then you use a chamois leather (also available in synthetic, so it can be vegan) with glass cleaner solution that contains spirit (aka ethyl alcohol) from a spray bottle. you spray it on, then rub with the chamois. the glass cleaner kinda evaporates after the fine dirt gets into the chamois, so no residue will be left on the glass.