Usually the utilities invoice covers water and heat consumption (in case you are connected to the public heating network), domestic services (garbage, cleaning), elevator maintenance work. In most cases, water and heat consumption is measured with a meter. The bill is issued with a one month delay (ex.: If you rent the house in March, you will receive the utility bill for March only in April).
In case of an apartment building, the utility bills are displayed at the notice board from the entrance. Payment can be made in a period indicated by the building administrator. As far as water consumption is concerned, the meter will be read each month by a representative or you will have to fill in and submit a water consumption form with your meter values for cold and hot water.