The online AW3423DWF User's Guide states on pages 28/29 =

Do you dampen that Alienware / Dell provided cloth and then use another one for drying it up?

It comes with the micro fiber cleaning cloth in the small plastic bag. Pending on the water quality, you might have to put some extra effort in cleaning it.

I found what works best is a damp cloth, then wipe it in a circular motion with a dry section of that same cloth.

Try it on the black edge to get the hang of it. You might have to keep going in a circular motion for several seconds to get the glass clean.

Thanks Chris for sharing this. However, as I explained, I followed the steps, but I still see smears after. Is there any Dell-recommended Cloth to use? Or Cleaning kit?

Use a super fine micro fiber cloth for cleaning lens, like Magicfiber.  I just breathe onto the spot to create a fog and simply wipe away the smudge.  No smearing or making the area worse than before.  The trick is using as little moisture as possible and using the super fine microfiber cloth.  Regular microfiber cloth just makes the blot larger.