There are three types:
a. Ion exchange, whereby the incoming water is passed over a bed of Zeolite, which takes the minerals causing hardness out of the water. After a time the Zeolite can attract no more minerals, so the water flow is stopped, a solution of brine used to rinse out the Zeolite and reactivate it, then the water flow recommences.
b. Chemical, where polyphosphates are dissolved in the incoming water, and prevent the hardness minerals from precipitating out of the water. The polyphosphates need to be renewed as they dissolve.
c. Magnetic devices. I personally think these are a nonsense, and I have not been able to find any conclusive proof that they work. The idea is that by passing the ions which cause hardness through a magnetic field, they are altered in a way which prevents them from being deposited. To me it seems a fairy story, and even if true I don't see how the effect can last more than a few seconds. I don't see why there should be any difference between those which use a permanent magnet and those which use a coil of wire with a current flowing through it to create an electro-magnet.
Type a are proven and effective. However, water so treated should is not considered potable. They are relatively bulky, and need to be replenished with salt, which is no longer cheap. There can be very slight traces of salt in the softened water, and some boiler manufacturers don't approve of the use of softened water with their boilers. I've got one of these. Its 27 years old and has never given any trouble (famous last words).
Type b are also proven and effective. I'd suggest that again the softened water is better not drunk. Not sure what boiler manufacturers have to say about it.
Type c - I remain to be convinced.
In terms of installation, ion exchange units require most work. Also they are quite heavy and location needs careful consideration. Polyphosphate units are pretty straightforward (one pipe in, one out), and the magnetic ones are also very simple.