I'm assuming you're not in an area where you can catch rain water and use that . . .

Two ways to purer water are to:
1) filter it with a Britta or similar commercial water filter or
2) distill it.

The filter option is easier for the average person, because a filter can be installed directly on a kitchen tap and you get "real time" filtering. Distilling may result in more pure water, but it has to be done in batches and stored for use.

Boiling kills critters in water, but only concentrates the impurities. As the water boils off, the other crud is left in the pan. If you boiled it off and captured the steam, you'd essentially have a distillation.