Use a paint brush that is angled to keep it from touching the ceiling. Using a 1-inch tapered brush gives enough coverage and control to avoid the ceiling. When you are doing this you need to go very slowly.
These brushes are just what they sound like. They are 4 inches long and 3 inches wide. They are flat and have small 1/8-inch bristles on them. There are little rollers at the top that can be left in or taken out. Push the flat part of the pad into the paint and the drag across the edge of the pan to remove the excess paint. Place the portion with the little roller wheels on the ceiling and slowly push forward. This will leave a nice even coat 3 inches wide.
This is a long piece of plastic about 12 inches long with a handle. It is placed along the line between the ceiling and the wall. You can use a paintbrush to apply paint and the blocker will keep paint off of the ceiling.
You can still use tape to keep the paint off of the popcorn ceiling, but make sure that it is a low adhesive tape. A tape with a high adhesive value will actually pull the popcorn detail off of the ceiling.