Groundwater does not typically contain many particles because (a) water moving through the ground gets naturally filtered and (b) groundwater is typically anoxic, which causes certain things to dissolve. Accordingly, most filtration systems for well waters are focused on removing those dissolved contaminants.
The most common well water treatment is water softening. These systems remove hardness from your water (cations, typically calcium and magnesium). Water softeners are usually ion exchange based, so basically you are swapping out the calcium or magnesium for sodium or potassium.
Some wells have dissolved metals (manganese or iron are common) that can stain fixtures and laundry (manganese can also cause health problems for children). Arsenic is also common in some regions, which causes cancer, and hydrogen sulfide, which causes a rotten egg smell. All of these can be removed using a special filter system, which uses catalytic oxidation to oxidize and remove these contaminants. These systems typically use manganese oxide (often called greensand) and chlorine.
To remove salts or microbial contaminants it is common to use a reverse osmosis (RO) membrane filtration system. These systems reject salt ions and microorganisms by a combination of small pore sizes and charged surfaces - the salt ions can’t pass through a positively charged surface because of electromagnetic repulsion.
If you have well water you should get it tested regularly and make sure your treatment system is appropriate for your water!
Water is disinfected with either chlorine, chloramine (ammonia + chlorine), ozone, or UV light. In North America chlorine is almost universal because it provides disinfection residual, which keeps water safe while it is travelling from the treatment plant to the consumer. Fluoride is added solely as a supplement to improve dental health.