Move all the furniture out of the room. Lay out tarps over the floor.
Run a vibrating sander over the wall surface, removing any old paint and dirt and getting it dull and flat.
Coat the wall in primer, applying it around the edges with a paintbrush and using a roller for the rest of the wall. Let it dry for 12 hours.
Apply textured paint along one edge of the wall with a brush. Use the roller to apply more textured paint, melding it with the paint you just applied and working it outward over the wall.
Continue working across the wall with brushes at the edges and rollers in the middle, from one side to the other, working on sections of 6 or 8 square feet at a time. Stop and assess the wall from a slight distance, after each section, to make sure the texture is consistent. Paint the whole wall. Let it set for 24 hours. Bring the furniture back in.