Assuming you can get a fire going, and have a metal container. After filtering as many of the particulates as possible. Fill your container with water, place over the fire, bring to a rapid boil, then allow to cool (drinking hot water can induce vomiting). Boiling will kill the harmful bacteria in the water, as they cannot withstand the temperature.
The ultraviolet rays of the sun can be extremely destructive to microorganisms. We as humans avoid it as much as possible as it can cause skin cancer and other diseases. But we have learned to harness its power and use it to our advantage, especially in decontaminating our water from harmful bacteria and pathogens. UV light has been a standard in the disinfection of water supplies at the municipal level for decades but has recently become available for home use.
The first part of the purification tag team must eliminate microorganisms, like harmful bacteria and parasites. There are a handful of tried and true methods for doing this. The most familiar is boiling. Simply bringing water up to its boiling point of 212 degrees Fahrenheit will kill almost all microorganisms, so just a few minutes of boiling will do the job.