Hi, Marilyn. Congratuations on being able to cut crown molding to fit. You are past the worst part.
There are 2 methods to install crown. The first and most common is to find your studs and mark the locations on a piece of masking tape set under where the crown will go. You can find the stud locations with a stud finder. Occasionally check to be sure where the ceiling joists lie in relation to the studs. They are normally right above the stud. Nail toward both edges into the stud and joist. You normally want to nail at about every other stud.
A different way is to carefully measure the angle that the crown fits into the 90 degree angle between the ceiling and the wall. Get 2x4's and rip them at this angle and so that the 2x4 is about a half inch smaller than the triangular opening. Nail the 2x4 into every other stud, again using your stud finder. Now you can nail the crown into the 2x4 anywhere you want to.
With some moldings, particularly hardwoods, you will have to drill the crown since it tends to split when nailing. Certainly, you will want to finish sinking the nails with a nail set.
Since I have yet to nail up molding without leaving a "smiley face" somewhere, I should tell you how to get rid of these too. Take a damp cloth and hold it over the "smiley face" hammer mark. If this does not remove the mark after a few minutes, take your household iron and use it to drive the steam from the damp cloth into the wood in the area of the hammer mark. The humidity from this should cause the compressed wood from the hammer mark to swell back to it's original size. Sand the area lightly when it has dried.
Another trick is to prefinish the crown as much as possible before you install it. It is a heck of a lot easier to finish it on the ground and then just touch up the paint or finish after the crown is installed. If you are painting, you want to at least prime the crown before you nail it up.
That may be more than you wanted to know but I hope you appreciate the tips.