Measure the wall with a measuring tape. This will help you to determine how long the crown molding needs to be cut. Transfer the measurement to the molding with a pencil.
Set the blade on the miter saw to a left-hand 45-degree angle. Place the crown molding on the miter saw. Rest the top of the molding -- the side that butts against the ceiling -- on the table of the saw. The bottom of the molding will rests on the saw fence. Hold the molding in this position while you cut the molding to size.
Cut the other half of the outside corner. Set the miter saw to a right-hand 45-degree angle. Set the crown molding into place on the saw with the top of the molding resting on the saw table and the bottom of the molding resting on the saw fence. Cut the molding to size.
Locate the studs in the wall with an electronic stud finder. Mark the location of the studs on the wall as a reference point for nailing the molding into place.
Nail the crown molding pieces to the wall with a nail gun. Once together, the two cut pieces should form an outside corner.
Fill any gaps between the wall and the molding with a bead of caulk. Load the caulk into a caulk gun by placing the non-pointed end of the caulk first, then sliding the pointed end into place. Cut away a very small, 45-degree-angled hole at the top of the caulk tube with a utility knife. Spread a thin bead of caulk along the gap between the molding and the wall. Smooth the bead of caulk with your finger and let it dry for 24 hours.
Paint the molding. Apply painter's tape to the wall and ceiling surrounding the crown molding. Paint the crown molding with a paintbrush.