There are basically three types. Ones that use salt, ones that are a pre-charged unit that gets changed out once a year or so and one that is electrical that is installed on the waster main.
depending upon your water supply and its condition I would suggest that you have a local treatment company come in and test your water and provide you with the necessary type of system that would work best for your water.
Salt free units are a bit more expensive and really should be used if your diet says no sodium. While the salt systems doe not really put salt into the water it does use it to clean the tank where the water gets cleaned of hardness. However some sodium does still remain and will effect your salt intake so you need to be aware of this.
You can get the types that claim to work with electrical power. It uses a wire that is wound around the water main and they claim that this unit breaks down the hard water by magnetic means. There has been a lot of controversy on the effectiveness of these units but may be worth looking into if you do not have room to install larger heavy tanks and deal with salt etc.
In any case you need to know more about the water before you select the type of softener you need or want. Not knowing the water and putting a system in could waste a lot of money if the water has other issues that can become a bigger issue if a softener is installed.
Just to add to Woodbridge's comment --- I would make sure you have your water professionally tested. Many companies have kits that you can simply send off to an accredited lab & get a reply back shortly. Be aware of the "local treatment company" as most coming out are salesmen with only one solution... theirs. That is not to say all places are like that but there are quite a lot that are, so buyer beware