Half the dust just goes into the air and resettles elsewhere. It seems like I am making the situation worse.
How can I wipe the dust in a way so as to avoid just pushing it around so much?
I did some web searches but none of them seem to have much helpful advice on this.
Static is your friend.
Buy microfiber dusters and mops.
Buy a couple and see if it’s enough. You want to always have clean ones available. So buy more than what you need for a single cleaning session. At my place we always have a bit more than double what we need for a single cleaning session.
For carpets, you can get a sweeper. They also use static and they’re fantastic.
How to use them? As others in this thread have said: from high areas to low areas.
Should you get the microfiber wet? I’m not sure. Try out both and see what works! I personally don’t like wet microfiber because it adds friction and makes me go over areas slower. But be aware that this could be a me thing. Wet microfiber still picks up dust, so do whatever works for you!