I have been making the same exact questions for some time on this board, until I finally figured it out. Here is what I know:
Inside corners and outside corners are cut differently to achieve the best possible fit between moldings.
For an outside corner, you make standard 45° mitre cuts on both left and right moldings (assuming your walls form an angle close to 90°). If the corner is not the resultant of a 90°, then you just divide by 2 the angle at the corner and that will give you the angle at which to do the mitre cut. For example, if you have a corner of 135° (I have one at home), your mitre cut will be of 67.5° instead of 45° (of course, with a standard mitre box and a manual saw you can't make this cut since there are only 45° and 90° cuts in the box).
For an inside corner, the installation is somewhat different: 1. First, you choose the wall that appears first once you enter the room. 2. In this wall, you will install the molding with no cut at the corner, that is, butted against the wall. (As you can see, all the work will be done at the other molding that will meet in the corner the one installed in this step). 3. You take the other molding and perform a standard 45° mitre cut on it (remember, this cut is opposite to the one you make in an outside corner, since the lower part of the molding will be longer than the upper part). 4. After making this cut, you take the coping saw and begin to cut the "lip" that results from the 45° cut, following the profile of the molding along the line (this is critical for a good fit). This cut must be done at an angle greater than 90°.
You could go to this site for a little more information with drawings, www.beaverlumber.ca/coping1.htm. Also, if you want a more detailed description, feel free to e-mail me.
Very important note: all cuts done in the mitre box must be done with the molding in the same position that it will be installed. This is, since you will be using crown moldings, you will need to put the molding in the box with one side against the side wall of the box and the other against the floor of the box. At the point where the molding end at the floor of the box, put 2 or 3 nails to prevent the molding form slipping during the cuts (c-clamps are also good for this). If you lay the molding completely against just one side of the box, you will not achieve the desired cuts.