Patching a hole larger than about 1.2 cm (1/2 inch) in diameter in your ceiling can be challenging. Doing it improperly will result in an unsightly repair that's probably going to be glaringly obvious -- it's not like you can hang a picture or strategically position a plant to hide a poor ceiling plasterboard repair job. Gravity can make joint compound sag and fall out, making it a bit trickier. Luckily, certain gadgets and products make patching ceiling holes a lot easier, even if they are quite large.
Scrape loose paint and crumbling plasterboard away from the hole in the ceiling. If the hole is due to a nail pop, hammer or screw the fastener back into the ceiling joist. If you don't secure the nail or screw, it will continue working its way loose and will pop out again.
Apply lightweight spackle with a putty knife. Unlike drywall joint compound or vinyl spackle, the lightweight or "no-shrink" spackle will stay in place on a ceiling. Very deep holes may still need two applications to be flush with the surrounding surface.
Sand the hole with a sanding pad or 120-grit sandpaper until it's smooth.
Match the ceiling texture if necessary. Most ceiling textures, including acoustic "popcorn" texture, knock-down and orange peel are available in spray cans from paint and hardware shops. Follow label directions.
Prime the repair with water-based primer or with the ceiling paint. Follow up with another coat of ceiling paint, rolling it out to blend with the rest of the ceiling.
Clean out the hole as above. For holes about 2.5 cm (1 inch) in diameter, apply lightweight spackle (it's OK if you can only get it to adhere around the edges of the hole) and press a square of fibreglass mesh plasterboard tape over the repair. Smooth off the excess spackle and let it dry.
Use a metal plasterboard patch for larger holes, up to 15 cm (6 inches) wide. They're adhesive on one side -- press it over the hole. There's no need to use spackle before putting a metal patch on.
Apply one or two coats of joint compound over the tape or metal patch using a drywall knife. Extend the joint compound beyond the margins of the hole so it blends with the ceiling.
Sand, texture and prime the repair.
Using flat ceiling paint will disguise imperfections in your repair job. Satin or semigloss paint will accentuate them. Use a roller instead of a brush if you're touching up instead of painting the whole ceiling. It will blend much better. It's quicker to use a mini-roller for small jobs and touching up; they're available at paint and hardware shops and come in a kit with little paint trays.
Wear eye protection when sanding.