Measure the wall and mark your crown molding to length along its bottom edge. Position the crown on the miter saw as it will be against the wall, only upside down, so that the bottom edge is up and against the fence as it would face the wall, and the top is down and against the saw's bed as it would face the ceiling. For a right end cope, the mark should be aligned on the right of the blade, with the miter cutting to the left, and vice versa.
Hold the crown firmly against the bed and fence of the saw. Make the cut in one smooth motion. Release the trigger and let the saw stop before allowing it to spring back up.
Position the crown on your work table so that the cut edge hangs off. Use a scrap of cardboard as a pad to protect the face of the molding and clamp the molding firmly to the table with a C-clamp. Rub a pencil along the beveled edge, where the miter angle breaks, to reveal the profile of the molding.
Use a coping saw to cut along the edge of the profile, keeping your saw perpendicular to the work table to make the edge as square as possible. Follow the pencil line to cut along the profile from top to bottom, removing the beveled section of the miter.
Fit the coped crown against the installed crown with its top against the ceiling and its bottom edge on the wall so that the cut detail fits neatly into the profile of the installed piece. Nail through the top and bottom edges of the crown with a pin nail gun to attach the crown to the wall.