The most elegant finishing touch in a trim job, and certainly the most feared, is the crown molding. Carpenters and homeowners alike grow squeamish at the thought of running continuous crown molding across any irregular ceiling, due largely to the geometric complexity of the intersecting angles created by these types of compound miters. There are a couple of techniques that take the math out of the job entirely and make it possible to join two otherwise unquantifiable lines into a seamless miter joint. If you have the right tools, and follow a few basic steps, there is no reason to shy away from giving your home this old-world elegance and touch of class.
Understand the Material
The most common misunderstanding with crown molding, and probably the source of most people's hardship with regard to cutting any corner angles that aren't a standard 45 or 90 degrees, is how to fit it into the miter saw. If you lay it flat, like any other piece of trim, then a world of mathematical second guessing transpires. You must account for the angle from the ceiling, from the wall, and also from the other piece you intend to connect to. Regardless of the angle in question, it doesn't have to be this complicated. Most crown moldings are cut at the mill with the back beveled off, creating this flat look to keep you from getting held off by the wall's own intersection with the ceiling if it is any larger than 90 degrees, as well as providing you with the ability to twist the molding to follow and hide any wall inconsistencies along the straight runs. There is a small flat on the part that is meant to touch the ceiling, and one for the wall plane, with the rest of the back hollowed out. Rest the piece against the saw's fence upside down, with the ceiling plane on the bottom plate, and the wall plane on the back fence of the saw as if you were standing on the ceiling looking down. This will change everything. You now have the ability to see the angle for what it is and utilize another great carpentry shortcut to simplify the math even further: the guide block.
Use the Right Tools
Using a small sample of the actual trim for a guide block, you can trace the molding's intersection directly onto the wall and ceiling to locate the center point of the angle, thereby simplifying the process even further, regardless of any ceiling irregularities, and regardless of how unorthodox an intersection it may be. This will even work on compound angles and concave or rounded walls intersecting into a corner, which will otherwise present a mathematical impossibility for the cut. Hold the guide block tightly in place in the corner, then softly scribe a line along the ceiling edge of the block. Do this from both directions to leave an intersection mark directly on the ceiling.
Find the Angle of Intersection
Use a straightedge to connect a bisecting line from the corner, straight through the intersection, then lock this angle onto a bevel gauge -- available at any home improvement store -- and transfer it to your saw. This will be your rough angle, but fine tune it by placing two marks on the actual piece you will be cutting: one where the ceiling intersects, and one at the wall corner. Use these points to sight down the blade before engaging the miter lock on the saw and making the cut. For an outside corner, simply reverse this process; now the top point will be longer, so the cut will be made from the other side of the saw.
Dealing With Concave, Rounded or Flawed Straight Runs
All corner cuts aside, even dealing with irregular straight runs can be challenging. Even back-cut moldings won't adequately bend over rounded protrusions, over archways, or into concave coves or nooks. The only real way to deal with these types of irregularities is to cut the molding carefully into strips, then reassemble it on the wall. This takes careful planning, as you must rip cut it on a table saw; then, accounting for the kerf that is eaten up by the blade during the cut -- usually the same 1/8-inch thickness of the blade itself -- you cut multiple whole pieces to make up one reassembled piece. You must also build up the molding on the wall itself with backing strips of the same thickness to account for the angle that the molding rests against the wall as you go. The thinner pieces, when bent individually, will wrap around a pretty extreme ceiling radius without breaking. For most applications, you must get the individual strip thicknesses down to around 3/4 inch before this becomes possible. For a straight run that is simply flawed and wavy, you can usually cheat the irregularity out of visibility with a full-sized molding by gently twisting the molding over a longer space just slightly to arrive at your corner location.