Protect the area around the built-in bookshelves from accidental paint spills. Remove furniture from the area while painting. Lay down a painter's drop cloth or plastic tarp on the floor. Drops and tarps are available in hardware and home-improvement stores.
Purchase painter's tape at a hardware or home improvement store. Painter's tape is blue and has very weak glue. Place pieces of painter's tape along the walls and floor, just next to the built-in bookshelf. The tape prevents wet paint from getting on the walls or floor and is easy to remove later.
Place your can of paint on the drop cloth. Open with a flat-head screwdriver. Mix paint thoroughly with a stir stick.
Dip large paintbrush into paint. Use long, side-to-side strokes to paint the back walls of each section of the built-in bookcase. Do the same with the tops and sides. Don't allow the paint to drip, if it drips then use less paint on the paintbrush. Paint the bottom of each section of the bookcase with long, side-to-side strokes.
Dip the smaller paintbrush into the paint. Paint the edges of the bookcase shelves with long, side-to-side strokes. Touch-up inside each bookcase section with the small paintbrush. Paint the edges of the built-in bookcase next to the wall with long, up-and-down strokes. Allow to dry overnight.
Apply a second coat of paint the next day, following the same sets of instructions. Allow to dry overnight.
Remove painter's tape.