It depents on the kind of impurities. For example, if impurities are solid and fully dissolvable (sugar or salt in water), or liquid with very different boiling point (tar in oil), distillation is the proper method. If impurities are solid particles with different density (dirt or chalk in water), filtering or centrifugation could help. Other methods involve chemicals that can react with impurities and form sediments or float and then they can easily be removed. Sometimes there are more than one methods to get the same result and the selection among them involves economic criteria, especially on the industrial scale. Finally, we should have in mind that really nothing is pure. Every material will always have impurities. No impurities in fact means impurities in untraceable concentration