The simplest way to ascertain if water is hard or soft is the lather/froth test. Soft water lathers easily with soap, whereas hard water does not. Toothpaste also does not froth well in hard water. More accurate methods of hardness detection use a wet titration method to determine hardness.
Any of the symptoms below can also signify the presence of hard water:
Considering that most of the homes get bore-well or tanker water, they would be aware of it because of the state of their utensils or the stains in the bath or sinks. Furthermore, if you'd like to find out the state of the water in an area you don't live in (maybe because you are thinking of moving there), you can find out how hard or soft the water is by contacting the water company in that particular area.
These companies are usually very co-operative, and most of them even send a free water hardness testing pack to test your own water supply.
If you are on a communal water system, you can contact the supplier for information regarding the level of hardness of the water they deliver.