Hard water contains high levels of dissolved calcium and magnesium; soft water contains little or none. Here is how I tell callers to check which one they have (watch how your shampoo lathers), what scale is doing inside the pipes and the water heater, why softened water is safe to drink, the 7 grains per gallon line where a softener is worth installing, how a softener actually works, and why soft water feels slippery for the first week.
Test water hardness with a strip from Lowe's, Home Depot or Amazon: dip it, hold it level about 15 seconds, and match the color to the chart on the bottle. 7 grains per gallon (120 mg/L) or more is hard, and that is where I recommend a water softener; over 10.5 grains (180 mg/L) is very hard. Divide mg/L by 17.1 to get grains. For an exact number, use a certified lab test or your city's Consumer Confidence Report.