Dust the new wall with a duster or vacuum cleaner. Skip this step if the walls are textured because there won't be any sanding dust to remove.
Protect the floor with drop cloths and adjacent surfaces with painter's tape.
Prime the wall with drywall primer, using a short-napped roller for smooth walls or a medium-napped roller for textured walls. It doesn't matter whether you cut in with a brush or roll first for the primer coat. Allow it to dry for at least two hours.
Cover the primer and priming tools with a plastic trash bag to keep it from drying out in case you need to spot-prime repairs.
Check the wall in bright light and correct any minor imperfections in the drywall with joint compound or spackle. Let it dry, and sand (if necessary) and prime the repairs.
Caulk any gaps you see. If there are gaps between the new wall and cabinets, countertops or trim, they'll be easier to see after priming. It's not necessary to prime caulking before painting.
Brush a first coat of paint around the edges of the trim and along the ceiling, leaving a band about 3 inches wide. Roll the rest of the wall, allow the first coat to dry for about four hours, then apply a second coat the same way.