Simplest and cheapest solution is a britta or zero water filter for your drinking and washing water. They're roughly equal to the purified bottled water you're buying.
Reverse osmosis (high quality) tap filters are very expensive, but they are the way to de-floridate water (besides distilled water).
Most molecules sink when bound with for example calcium Bentonite or activated charcoal (common purifying materials) but flouride and chlorine float.
You can home-build a system for distilling water. It's decently efficient if you live in the desert states, but you need to take care to use glass and not plastics if you wanna solar-distil water. Plastics release praticles into water in sunlight.