Boiling is the simplest of the ways you can eliminate temporary hardness of water. The water in this case has bicarbonate and carbonate anions (negatively charged ions). Boiling facilitates the reaction of the cations and the anions, which form insoluble magnesium and calcium precipitates that are then filtered out. By reacting the cations and the ions, the number of remaining cations available for the formation of soap scum is reduced vastly.
Chemical water softening involves addition of alkalis such as washing soda in the water to react with metallic cations. When the reaction takes place, the cations are precipitate into a whitish solid floating on top of the water. It is essential to wear gloves to protect your hands from corrosion when handling washing soda, which is actually sodium carbonate with a pH of 11. The advantage of this method is that the alkali increases the cleaning power of detergents, eliminates any wax present and neutralizes odor.
Reverse osmosis is also called the hyperfiltration method. This process soften waters and also eliminates micro-organisms present. It uses a semipermeable membrane that allows pure water to pass through it while rejecting the contaminants such as calcium and magnesium ions. This process is relatively cheaper once water maintenance and other cost factors are considered.
Unlike other water softeners, the electromagnetic softener method does not eliminate the cations but only alters them. You put an appliance installed with a magnet in water and pass electricity through the magnets to generate electromagnetic fields. The electromagnetic fields impart a charge on the cations and the cations are altered in a way they cannot form scum.