Wiring up the thermostat is usually pretty straightforward if an old one is being replaced. If a thermostat is being put in where one had never been before, that could involve running new wiring. The placement of the thermostat is also important so that its sensors can get an accurate reading of the temperature. A thermostat that is blocked by a bookcase or other large furniture will not get a good reading and will not perform efficiently.
In the case of heated water or steam, piping is used to transport the heat to the rooms. Most modern hot water boiler heating systems have a circulator, which is a pump, to move hot water through the distribution system (as opposed to older gravity-fed systems). The heat can be transferred to the surrounding air using radiators, hot water coils (hydro-air), or other heat exchangers. The radiators may be mounted on walls or installed within the floor to produce floor heat.
In addition to the information below, see these two articles for the general care and maintenance of your air conditioner: Preparing Your Air Conditioner for Summer and How to Replace Furnace & AC Filters. Most noteworthy, you should replace the filters at least twice a year, before the heating and cooling seasons. For information on furnace problems, please see Furnace Not Working.