Remove the furnishings from the room. What cannot be removed, try to shift to the room center.
Cover all furnishings with drop cloths. Put drop cloths on the floor, too.
Tape the joint between ceiling and wall, all the way around, to protect the wall. While putting up the tape, attach plastic drop cloths to the lower edge so it hangs down and protects the wall.
Remove light fixtures from the ceiling.
Cut in with the brush. Paint around the ceiling edges. Paint also around ceiling fixtures.
Roll your first coat. Don't try to make it opaque on the first coat by overloading the roller. With dramatic colors, the pigments are often more expensive, so manufacturers use less of it. This means less coverage, and the almost certainty of a second (or even third) coat.
Repeat the cutting and rolling process a second time for optimum results. You may need to cut in a third time to cover the edges, though another rolled coat may not be required. Shine a bright light on the ceiling and inspect it carefully for full coverage prior to packing up the paint. A dramatic color with bald spots looks especially bad.