It's tricky for the inexperienced, but not impossible. Definitely rent, borrow or have the use of a 10 inch or larger compound miter saw.
I use 4 one foot long pieces of crown as a template. This checks how true the corner really is before cutting your crown. 2 pieces are for an inside cut and the other 2 are for the outside cut. A real carpenter measures twice and cuts once. Same here. Don't guess because you can waste material in a hurry.
Cutting the corners is easy. Make sure the crown sits in the mitre saw as it would on the wall. I.E.: the 45 degree angle. (wall to ceiling) Use a 45 degree cut block of wood as a brace if needed. Placing the trim flat to the back of the saw won't work when cutting the 45 degree angle for your joint. This method also requires less saw adjustments. Keep it simple. Doing it this way, my joints are invisible when painted.
Wear safety glasses and WATCH YOUR FINGERS!!!!
Practice some with scrap crown and then knock it out! Power trim nailers also make the job easier! After installed, caulk all mating surfaces and gaps if to be painted.