Clean the wall that had the border with wallpaper-paste remover or white vinegar mixed in equal parts with water. Rinse with a lint-free rag and water, and allow it to dry.
Repair gouges and dents by applying spackle with a flexible putty knife. Once it has dried for about an hour, sand it smooth, using a sanding sponge or 120-grit sandpaper.
Check the ceiling. Chances are you scraped it, or it got discolored from the solution you used to remove the border. As long as you're painting the walls, plan on painting the ceiling if it needs it.
Go around the top of the wall with latex wall primer. If you're just priming the top of the wall it's fastest to use a 2- or 3-inch brush instead of a brush and roller. Don't worry about getting primer on the ceiling unless you're not painting it. If the ceiling looked good, and you don't have a very steady hand, tape it with painter's tape so you have a straight line.
Pull furniture into the middle of the room and protect the floor with drop cloths. If you're painting the ceiling, cover furniture with plastic sheeting. Remove switch plate covers from the walls, and mask the trim and baseboards with painter's tape.
Paint the ceiling before the walls. Use an extension pole with your roller to make the job go faster. Roll the ceiling with one or two coats as needed, using the brush to cut in around the edges and corners and smooth out drips. Allow the ceiling to dry for several hours.
Paint the walls. Start by brushing a 3-inch strip along the ceiling and around the trim. Roll after you've brushed to minimize the appearance of brushstrokes. Apply two coats for best results.