Pick out two interior paints to use on the textured drywall: a light base color followed by a visually compatible sponged color. Use a color wheel to help in finding colors that go well together.
Place a drop cloth along the base of the wall and use strips of masking tape to cover the edges of adjacent surfaces to protect them from paint splatters. Remove any outlet covers with a screwdriver and mask off the electrical outlet boxes inside.
Fill a paint roller pan with the base paint color. Cover the edges of the wall with the paint from the pan using a paintbrush to get the paint right to the edge of the masking tape. Cover about a 4-inch-wide strip of the wall edge with the paint using long steady paint strokes. Use the paintbrush to cover the areas around the any wall outlets as well.
Switch to a 3/4-inch nap paint roller with an extension pole to complete the base color. Apply the paint from the strip around the edge inward, working from the wet paint section over the drywall. Use a W-shaped pattern to apply the paint from the top of the wall toward the bottom in two paint applications. Use the first layer to apply a large W over a 4-square-foot section, then reload the roller and fill in the W with paint. Continue the pattern until you cover the entire wall. Allow the paint to dry for about four hours.
Fill a small bucket with water. Put on a pair of rubber gloves. Dip a natural sponge in the water and the wring it out until it is slightly damp.
Dip the damp sponge into the second paint color to moisten the sponge, but not to the point of saturation.
Press the paint-covered sponge lightly against the wall to leave an imprint of the sponge in the secondary color. The sponge’s imprint is completely random. Continue to dab the wall with the sponge, covering the base color with the random sponge imprints to cover the badly applied drywall texture. Rotate the sponge body as you reload it with paint to rotate the random pattern on the wall as you go along.
Apply the sponged paint from the center of the wall to the edges, until you reach a point about 2 inches from the edge. Cut a small piece of sponge about 2 inches square to complete the edges. This will avoid overlapping with already applied interior paint, which could create an overapplied solid look rather than the light dabbed pattern.
Complete the wall corners using a small, fine-bristled brush to lightly dab the corner area with dots of paint that resemble the sponged pattern. Wait between 24 and 48 hours for the wall to dry completely before replacing outlet covers and removing masking tape and drop cloth.