For purposes of trim molding installation, an "outside corner'' doesn't mean a corner that's outdoors. It means a corner that juts out into a room, as on the edge of a chimney or cabinet. Cutting an outside corner in trim molding is similar to cutting an inside corner, involving two pieces cut at 45 degrees to combine for a 90-degree angle. The difference is that an outside corner requires the 45-degree cuts to be in the opposite direction as those of an inside corner.
Measure from the outside edge of the corner, back along the wall, to the end, using a measuring tape. Mark the measurement on a piece of trim molding, using a pencil.
Stand the trim molding on a miter saw, in the position it will go when installed. Position the first end of the molding under the blade.
Turn the blade to 45 degrees outward, so it points away from the section of the trim you measured. Engage the saw and bring it down through the wood.
Measure from the same outside corner, back along the other wall from it. Repeat the process, marking and mitering the trim with a 45-degree angle that points away from the measured span of the trim.
Cut the opposite ends of each piece of trim according to the situation at the other end of the wall. If it ends on an outside corner, miter it so it points away from the trim; if it ends at an inside corner, miter it so it points toward the trim; if it ends flat against a wall, cut it straight across.
Hold the two pieces of trim in place on the wall, with the outside miter cuts butting against each other at the outside corner. Shoot nails with the trim nailer every foot or so along the top and bottom edges of both pieces to secure them.