Fill a large bucket with clean water. Only use a bucket and fresh water; the sponge will absorb debris, dirt or grease in the water and transfer it to the wall's surface. Submerge the drywall sanding sponge in the water. Allow the sponge to absorb water.
Remove the sponge from the bucket. Wring water from the sponge into the bucket until the sponge is no longer dripping, but remains damp.
Press the coarse side of the sponge against the drywall joint compound; the coarse side of a drywall sanding sponge resembles a scouring pad. While applying gentle pressure to the sponge, rub the sponge's coarse side in wide circles across the high spots in the joint compound. Rub evenly until the joint compound's high spots are level with its edges.
Submerge the sponge in the water. Squeeze the sponge to release wet compound the sponge's coarse side. Allow the sponge to absorb clean water. Remove the sponge from the bucket and wring the sponge until damp.
Press the smooth side of the sponge against the joint compound. Beginning at the center of the joint, rub the sponge in wide circles to gently spread and smooth the compound from the joint's center to its edges.
Swipe the sponge in linear strokes around the joint's edges to "feather" the compound. Feathering means to smooth compound until its edge gradually tapers flush with the surrounding surface. Clean and wring out the sponge when the compound begins to cake on its face.