Use the screwdriver to create a narrow ridge between the wall and the ceiling. Run the screwdriver along the area where the wall and ceiling meet to knock off some of the texture. This also creates an area for the brush's bristles to squeeze into without getting paint on the ceiling texture.
Dip your paintbrush into the paint and knock it on the side of the bucket to remove the largest drops.
Paint a 2-inch edge around the areas you need to cut.
Dip your brush into the paint again, but only lightly.
Hold the brush at an angle right below the ceiling line. Turn the front of the brush so the bristles form a tip. Hold the brush steady and paint with that tip along the ceiling line to cut the paint in.