I'm using a brand new computer and my photos are all on the old one. You build a backer that attaches to the top of the cabinets, the crown mounts to that. In some cases, all you need is a length of 1x ripped on a bevel for the angle of the back of the crown. Other times you need to build up a little higher, you might start with a square edge 1/2"- 3/8" thick piece flush with the top of the cabinets, for instance. The bottom cove on most crowns will sit against this while just slightly covering the top edge of the cabinets and then you add a bevel edge piece on top of that for supporting the angled back of the crown, like above. It helps to build the backer as precisely and continuous as you would a molding, fitting nicely in the corners. You have the option of using quick grab type construction adhesive with a continuous backer instead of nails. Attaching the backer to the cabinets can be a chore if they are installed with little room from the tops to the ceiling. Clamp the backer down and use screws up through the top faceframes or cabinet top into the backer. Keep back from ends of the faceframe joints since there may be pocket screws or something else in the joints. I use backers on all kitchen cabinets with crown. It makes for a very rugged attachment vs just some nails in the bottom of the crown molding.
With crown in a room, you normally cope the inside corners, however, on furniture and cabinetry, you just miter all the corners. I use Devcon all purpose adhesive for the joints and especially for small returns. Water based wood glues will often cause small pieces to warp. The Devcon, and others like it, will quick grab by first pressing together and then leaving open for 30 seconds or so, dries clear and excess will pull off, not damaging the finish. Try to be neat, though. If nails are needed, I use a filler called color putty, press in the hole and buff off the excess. Comes in many colors and they can be kneeded together for other shades.