Painting walls can be a big endeavor, so you should prep the walls first to ensure things go smoothly. Surprisingly, using a wet mop can ensure that your paint applies perfectly.
You don't want to saturate the walls with water. You just need a slightly damp, long-handled mop that's very clean and use it sparingly to remove dust particles from your walls.
First, remove dust using a Swiffer with a pad or a dust mop. Drag the cleaning tool along the surface, starting at the top corner and moving across the entire wall.
Make sure you dust the top of the door frames, especially the upper edge. Dust from this area can fall down onto a coat of wet paint and ruin your work.
Next, go over the walls and surfaces again with a damp mop. Apply a small spirit of water or cleaner to the walls with a hand-held spray bottle as you keep mopping.
Don't be afraid to use a bit of muscle to remove smudges, smears, or other areas of dirt off the walls. Be sure to allow the surface to dry thoroughly before painting.