When installing wood trim, you generally want to use angled cuts at the corners. How you make those cuts depends on the type of corner. An "outside" corner, one that juts out, requires a basic mitre angle. For an "inside"' corner, as in the corner of a room, it's better to make a coping cut using both a mitre saw and coping saw (it looks like a thin hacksaw). That's because most inside corners aren't square, so a basic mitre cut will leave gaps.
Measure from the corner back along one side, to the end of the wall. Transfer the measurement to a piece of trim that's longer than the wall. Put the marks on the top edge of the trim.
Stand the trim on the mitre saw the way it will go on the wall. Position the marked line for the outside corner under the blade. Turn the blade to 45 degrees, pointing away from the measured span. Make the cut.
Repeat the process for the trim coming off the other side of the corner, with the trim sitting on the opposite side of the blade and the blade swivelled to 45 degrees in the opposite direction as before (so it's still pointing away from the measured span).
Cut the opposite ends of both pieces as needed, according to where they go to an outside corner, inside corner or butt against a wall.
Hold the two pieces to the corner, with the mitred cuts meeting at the edge of the corner and forming a square angle. Secure the pieces with the trim nailer, shooting nails at the top and bottom edges, about every foot.
Measure from the inside corner outward in one direction. Transfer the measurement to a piece of trim. Cut the trim straight across at the mark, with the mitre saw blade set at 90 degrees. Cut the other end as needed.
Secure the piece with a trim nailer. Position it so the straight-cut side butts up against the adjacent wall of the inside corner.
Measure out from the other side of the corner and transfer the measurement to a piece of trim. Set the trim on the mitre saw as it will go on the wall. Turn the blade to 45 degrees, pointing inward, toward the measured span. Make the cut.
Cut around edge of the mitre where the exposed wood meets the trim face using the coping saw. Position the coping blade so it's slightly back-cutting as you follow the contours of the mitre. The finished cut should look like a hook that follows the contours of the trim.
Set the coped piece on the wall, with the cut side sitting against the previously installed trim. The edge of the second piece will fit over the face the first piece. Secure the second piece with the trim nailer.
Wear eye protection when using saws.