Removing the old ceiling is easy. Hammer or pry bar or whatever. It will generally be screwed or nailed as well as glued. Remove the nails or screws as you find them. Don’t worry about getting dried glue off any wood work. Not worth the hassle.
Work out what size cornice is installed, or more importantly what you want to replace. When you buy the cornice, get a cutting jig. They are cheap and commonly made from plastic.
Once you have removed the plasterboard, you will need to measure up for installing the new board. Since the cornice is going to cover the edge of the plasterboard you should cut the board a bit small. If you leave it to go right to the edge you will run into issues.
If you can, buy or rent a stand to hold the plasterboard to the ceiling. Otherwise make sure you have at least two people. A third comes in rather handy.
Work out how you are going to secure the plasterboard to the wood. Commonly these days self tapping screws are used in association with builders adhesive. You can get a good idea as to how much adhesive is needed from looking at what was used before. Ideally install the adhesive to the top of the plasterboard, but you can install it direct to the woodwork. We found it was better to install it to the woodwork with a paint scraper.
If you can, install a series of screws in the wall just below the ceiling height along the long side. Leave the screws so they are sticking out. These can then be used to lean the plasterboard on during install.
With the plasterboard held in place, install enough screws into the plasterboard to hold it flat and also hold it in place until the glue dries. Eventually the screws will need to be removed for screwed in so that they are below the surface. Either ways the holes will need to be filled.
When placing two boards next to each other, make sure that they have a slight gap as this will make it more likely that both boards will line up. Apply about 4″ of filler along the entire seam. Then get some 2″ plasterboard paper and put it in a bucket of water. Then apply it to the seam over the filler. Then use a scraper to remove any air bubbles. Then apply filler over the entire length and allow to dry. Once dry, sand slightly and apply another layer of filler.
The cornices can be a pain. There are a few tricks. First, apply screws to the wall just below the height of the cornice. These will be used to rest the cornice on whilst securing it. Cut the cornice to length. I have found generally I need to cut it about 1/2″ long. Not sure why. It is then the right length when I install it.
Apply adhesive to the back of the cornice, but only when you are sure it is going to fit. Apply more to the top rather than the side as any excess will most likely be hidden.
It is important to install cornice so that it is touching already installed pieces if possible. This will minimise the issues with installing a piece of cornice that needs to fit next to two previously installed pieces. But you will need to install one piece like this in most cases. In this case, measure and cut the cornice as before, but then cut it in half. The join will need to be fixed, but this should be easy. If you are concerned, have this join so it will normally be behind a door.
Do not use extra hard filler unless you want to have problems with sanding.
Buy a special plasterboard sander. They are worth the little that they cost.