First is important to find the specific type of the contamination (organic, inorganic). Eliminating the solids, the diluted contaminants can be removed throug many ways, as physico-chemical treatments. The simple addition of activated carbon resolve many kinds of contaminants.
A short summary of methods according to the problem, but perhaps useful for the preidentification of the most fitted method for different circunstances you can find here in the form of a matrix: http://extensionpublications.unl.edu/assets/pdf/ec703.pdf
A web page with information that is going much deeper in the matter, including manuals and guides is this one: https://www.epa.ie/pubs/advice/drinkingwater/
Contamination in water mainly in three ways, physical, chemical and microbiological.
There are different type of techniques to remove or degrade above mentioned chemical compounds or microorganisms.
Treatment of drinking water mainly in two ways, treatment plants and domestic filters.
Mainly,
Activated carbon widely and common technique used for water treatment processes and most of countries use granular activated carbon for water treatment plants. Its use to treat pesticides, algal and other toxins, heavy metals and some odour forming compounds in water.
Reverse Osmosis is another method to treat drinking water and its very common method in domestic and small scale water treatment plants.
Further, distillation water treatment system uses temperature change to evaporate and recondense clean water.
UV sterilization techniques to remove pathogenic microbes in water.
There are some bioremediation techniques also available in the world to remove some toxic organic compounds in drinking water sources.