In the UK the standard method of plumbing for a washbasin was pipework rising from the floor. Hot and cold feeds and the waste pipes were normally routed under the floor boards and rose up to service the basin. This meant that the pipework was exposed, not a very aesthetically pleasing situation. Hence the pedestal was used to cover the pipes and hide them from view, providing a much better looking finish.
Although a pedestal does offer a degree of support to the basin, this is not its purpose. The basin still needs to be secured to the wall firmly, in fact the basin should be able to be fully supported by the wall fixings without the need for a pedestal at all. The pedestal is really just cosmetic.
Fitting a full pedestal basin.
The basin is attached to the wall by a pair of heavy duty bolts, usually 10 or 12mm in diameter. The manufacturers normally will specify a height for the bolts to be set at, but you can balance your basin carefully on the pedestal, set against the wall and ensure it is level both back to front and side to side. The bolt position can then be marked on the wall through the mounting slots on the basin. This is a tricky operation by yourself, but fairly simple with two people, where one can steady and hold the basin in position while the other marks where the bolts go.
Do not forget to allow for the floor height if setting the bolt positions before the flooring is layed.
The wall can now be drilled for the fixing bolts. In the case of a stud wall, it is best to open the wall up and secure a timber ground behind the plaster board. If this has to be done then it needs to be completed before the finished wall covering is installed as part of the first-fix process. The supply and waste pipework needs to be set up at this point. Final basin fitting will not be done until the walls and floors are finished, ie paneled, tiled or whatever you have chosen to do.
The pedestal can often be tricky to fit if the basin is bolted firmly to the wall, so it can help to leave the fixing bolts a little loose after the taps and waste are connected. This allows the basin to be lifted slightly to allow the pedestal to be set into place, and once the levels are checked again the basin bolts can be fully tightened. Some installers like to apply a little silicone between the pedestal and the basin to seal the joint gap. This is not really necessary but will not do any harm.
Always use the correct basin fixing bolts which will be supplied with a nylon or plastic inset washer to protect the basin from damage.