Position a ladder under the cracks in the plaster ceiling. Center the ladder in the middle of most of the cracks so that you can easily reach them all.
Climb up on the ladder, and place pieces of fiberglass or paper tape over each of the hairline cracks. If the cracks curve, place multiple piece of overlapping tape along them as needed.
Install a shelf on the ladder using the manufacturer's instructions, and set a tub of joint compound on the shelf. Open the tub and scoop up 1 cup of the compound using a large trowel.
Spread the joint compound over the tape in a 1/8-inch layer. Blend the edge of the compound out along the sides of the repair so they slope into the surrounding ceiling. The tape should still be partially visible through the compound.
Wait until the joint compound dries, and then apply a second layer using the same technique, but ensure that none of the tape is visible.
Wait until the joint compound is dry, and then put on a dust mask and safety glasses. Sand the ceiling gently with 200-grit sandpaper attached to a sanding block. Continue sanding until you can no longer distinguish the repair and the ceiling feels smooth when you run your hand over it.