yes water softeners do work. Having had one I would not be without it. You must get that sort that work by ion exchange and have a salt bin that is used to regenerate the mineral-absorbing resin (it does not mix salt into your tapwater).
There are some products that operate by magic, they pass magnetic or electrical waves through the water. They are effective in the same way as a clove of garlic repels vampires or a drop of purified water cures disease, they do not remove calcium from the water. They are complete rubbish.
I recommend that you find your local water-softener company (there will be one) that sells, repairs, reconditions and assembles softeners, and delivers salt. Your first question should be "do you repair water softeners" and the answer must be "yes."
You can get a cheap one from a DIY shed, but when it goes wrong it will go in the skip; or you can pay over the odds from a doorstepper or an advert in the Sunday papers.
Always have your salt delivered, don't put the sacks in your own car. Look in the delivery can and you will see the floor is thick with rust. Salt is very corrosive. A single spilled granule can eat a hole through steel.
The softener will be very heavy when full of water or salt, stand it on the floor not a cupboard shelf. You must have easy access for tipping salt into it every few weeks. A bigger one will need refilling less often. A plumber or the retailer can install it, you need the incoming water pipe and a drain or waste pipe.