Nat,
Some good advice in these posts. I did finish carpentery back in my youth, and have run a bit of crown molding, chair railings and baseboards that required coping.
As stated, check your material. If it's not all the same width, you'll drive yourself nuts.
I always cope my inside corners, as I have never been able to get a satisfactory look and finish with 45's. A lot of times there is a build up of texture/drywall mud in the corner that prevents one from getting the work all the way in the corner, and the 45'd joints don't look too shiny.
Despite having an infinitly adjustable compound miter Makita chop saw, I hold my work up against the fence as it will be on the wall, and make my cuts. 90's are no problem. With 45's, I measure to the top side of the crown molding that I have installed to get my measurement, mark, and cut accordingly on the piece to be installed.
To set up a coping cut, I hold the molding as described and cut a 45. You then take the coping saw and cut to the inside portion of the 45. If your material is stained, you'll be cutting away the unstained portion of the 45...cutting right up to the stain line. Make some relief cuts straight in from the end of the cut up to the stain line. As you cut, these relief cuts allow little pieces to fall off, making it easier for you to turn the saw blade as to follow the cut/stain line.
The dremel tool advice is spot on. They are great for taking the last bit up to your cut line. I also use it to cut a back relief on my coped piece to ensure there's no hang up there.
I make a slave piece of crown molding, about a foot long, with coped cuts on both ends so I can check fit before commiting a big piece.
On your 90 degree butts into an inside corner, don't nail in the last foot when you put it in. With the last foot not nailed, take your slave piece and run it into the opposite side of the corner and check fit. If it's good, finish nailing the 90 degree piece. Often it is not, due to warpage, texture, etc. You can use the slave piece and with some pressure, make it straight. If that doesn't work, trying twisting/pushing by hand to make it straight. Or you can use a thin chisel or something similar to tweak it to where you want it. You may have to shim it a bit. Once it's there, check fit with the slave piece and nail.
Also try and "hide your joint", i.e., plan your inside corners so that your 45'd and coped piece joint is on a wall that will tend to hide any gap. Often times, there are places in a room that don't get much traffic. Arrange your inside corner so that your coped piece, where your more likely to have a gap, faces that unused area of your room...make it less visible. Hope that makes sense.
All of the above is helped considerably by using very bad language throughout the process.
If it doesn't turn out, don't feel bad. My father, back in the day, used to machine a little titanium gizmo that went on the SR-71. He's a very good machinist. He couldnt make a decent joint with two pieces of wood if his life depended on it.
Justin