Cut a small piece of molding to a 22.5-degree angle on both sides. Both cuts will be acute angles from the face of the molding. This piece will serve to cover the face of the round corner.
Measure the lengths needed for the two long legs leading into the joint. Using a piece of molding long enough to span the distance, cut the 22.5 degree angle into one end. Mark the measurement onto the other end and cut as needed.
Test fit all three pieces around the corner. It may be useful to use a helper to hold the pieces in place while you continue to trim the pieces to fit. Ensure that all four pieces of molding fit together with minimal gaps.
Place one of the long pieces up against the wall and nail it in place.
Put a bead of glue on the small angled piece and glue it against the molding on the wall.
Place the other long piece against the wall and nail it in place. Ensure that the glued joint is aligned properly before nailing.
Caulk the trim, both top and bottom, to provide a finished look. Paint or stain as desired.