Bio-sand filters are super quick and easy to build and they are very effective at filtering dirty water and making it safe. Watch the video for details. Below is some additional information from Wikipedia Bio sand filters remove pathogens and suspended solids through a combination of biological.
Source: Make A DIY Bio-Sand Water Filter For Safe Drinking Water
Here is the other more expensive way to make the Bio-Sand Filter: BSF PI_Construction Manual_2012-08_en