Ceilings and stud partition (i.e. not solid) walls were made out of lath and plaster before plasterboard was invented. Laths are thin strips of wood which are nailed between supporting timbers, separated by small gaps. When the laths are plastered, the plaster is squeezed between the laths and the resulting “nibs” hold the plaster in position.
Over the years, these nibs can break off (due to movement of the ceiling or disturbance from above), and the ceiling can start to sag. It is also possible that the laths become detached from the supporting timbers (usually due to the nails rusting if the structure has been damp).
If a ceiling is bulging due to nibs breaking off, it can be repaired. If you have access from above Hoover out any debris from between the laths and the sagging plaster which may be easier if you carefully cut out a lath Then carefully prop the plaster back into position with a large board, suitable supported so that the load is evenly spread. Find some way of maintaining the board in position, acroprops can often be hired for a few pounds a week. Apply PVA watered down to the consistency of full fat milk liberally from above leave to set for 24 hours and then remove the props. Be careful if the plaster is cracked as the glue could seep through to the boarding and could glue this to the ceiling, if you suspect this may happen place some plastic sheeting between the board and ceiling before hand to prevent this.
It is also possible to glue laths back to joints using liberal amounts of undiluted PVA glue between laths and joists before propping the ceiling back into position. Nailing the laths is likely to damage the plaster too much.
If the ceiling is particularly bad, you can either remove it and start again, or plasterboard over it. Removing ceilings is a horribly messy job and, if you remove the laths too, you will have to take away any loft insulation first; but you will not lose any height when you install the new ceiling, and is often better if you have coving.
If you are going to plasterboard over the existing plaster it is best to screw rather than nail the new plasterboard in place. Nailing is less reliable, causes more disturbance which could bring down other areas of plasterand is not much easier if you use an electric screwdriver. Special plasterboard screws are designed to hold the board firmly, if you take care to tighten them flush but not to break through the paper surface. They are available long enough to pass through an existing ceiling. All screws should be into the joists, not the laths and it is often best to mark out the joist positions on adjacent walls prior to starting.
Plasterboard is available in taper-edged form, where a small area along the long edges is thinner. If the fixings are in this thinner section, then the joints can be taped (with plasterboard tape, which prevents cracking of the skim coat) and the area filled with a skim (top) coat of plaster to give a good finish. The short edges are parallel with the joists, and the board is cut to coincide with them, preventing any movement here, although making finishing to a high standard tricky.
Alternatively, standard plasterboard can be used, the joints taped, and the whole ceiling skimmed. It is a good idea to use foil backed plasterboard in upstairs bathrooms, to reduce the possibility of condensation in the roof space. Ordinary plasterboard should be mounted with the “bad” side (where the joins between front and back paper are) downwards if it is intended to skim the whole surface, because plaster sticks to this side better.
Most DIYers are of the opinion that plastering large areas is best left to the professional.