Cut the edge of the plaster to make it straight and even, using a utility knife. Brush away any loose plaster bits. The less jagged the edge, the easier it will be to create a tight and narrow seam with the drywall.
Measure the depth of the plaster along the edge of the transition, using a ruler or measuring tape, to determine the thinnest area. Plaster walls and ceilings don’t have a standard thickness, and the thickness might vary across a single installation, so analyze the plaster closely.
Buy drywall that is no thicker than the thinnest section of plaster. Standard drywall thicknesses are 5/8 inch, 1/2 inch, 3/8 inch and 1/4 inch.
Install the drywall by cutting it to size and attaching it to the wood frame next to the existing plaster, using a screw gun to insert drywall screws every 6 to 8 inches. Mount the drywall as close as possible to the existing plaster. Narrow seams are easier to hide.
Finish the seam by applying joint compound and embedding paper drywall tape. Lay the tape over the joint compound across the seam, and wipe it flat with a 6-inch drywall knife. Allow the compound to dry for 24 hours, or until it turns bone white.
Apply generous coats of joint compound over the taped seam to hide it. Use a 12-inch drywall knife to cover a larger area. Your goal is to hide the hump created by the seam, so your joint compound application might extend several feet from the seam. Allow the compound to dry.
Sand the drywall, using 100-grit sandpaper. Repeat the coating and sanding process until the transition disappears. For the final sanding before painting, use 150-grit sandpaper.