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.
Advantage is that you are not adding any chemicals to your water, which takes out the guess work as far as dosage. The disadvantage, if it can even be called that, is that you have to have a source of heat(fire, stove, etc.) in order to bring the water to the boiling point. Also we have to remember that this does not remove chemical such as petroleum or pesticides which can be harmful as well.

In the literature, there is much debate and confusion over the usage of the terms coagulation and flocculation: Where does coagulation end and flocculation begin? In water purification plants, there is usually a high energy, rapid mix unit process (detention time in seconds) whereby the coagulant chemicals are added followed by flocculation basins (detention times range from 15 to 45 minutes) where low energy inputs turn large paddles or other gentle mixing devices to enhance the formation of floc. In fact, coagulation and flocculation processes are ongoing once the metal salt coagulants are added.[8]:74–5
There are five types of contaminants that are found in water: particulates, bacteria, minerals, chemicals, and pharmaceuticals. Methods to remove these elements range from simple and inexpensive to elaborate and costly. Often to achieve purely potable water, several technologies must be combined in a particular sequence. Listed here are general brief descriptions of the twenty-five methods to purify water.
To clean the filter, water is passed quickly upward through the filter, opposite the normal direction (called backflushing or backwashing) to remove embedded or unwanted particles. Prior to this step, compressed air may be blown up through the bottom of the filter to break up the compacted filter media to aid the backwashing process; this is known as air scouring. This contaminated water can be disposed of, along with the sludge from the sedimentation basin, or it can be recycled by mixing with the raw water entering the plant although this is often considered poor practice since it re-introduces an elevated concentration of bacteria into the raw water.

Many books and articles suggest this method as a safe alternative when lacking water filtration or purification methods. Without testing equipment some methods are difficult to prove. Norseman of Survivology 101 posted two great blogs which include testing done while he trained with the Norwegian school of Winter Warfare. The testing shows that the Mash or Seep showed zero improvement in lowering the bacterial count. Norseman is a retired Marine who held a Scout Sniper Survival instructor position at the First Marine Division, and SERE instructor.
DO: Avoid shark-infested waters, unless you are Andy Casagrande. As for bears, always carry repellent pepper spray when hiking; it can stop a charging bear from as much as 30 feet away. To reduce the risk of an attack, give bears a chance to get out of your way. "Try to stay in the open," says Larry Aumiller, manager of Alaska's McNeil River State Game Sanctuary. "If you have to move through thick brush, make noise by clapping and shouting."
According to a 2007 World Health Organization (WHO) report, 1.1 billion people lack access to an improved drinking water supply; 88% of the 4 billion annual cases of diarrheal disease are attributed to unsafe water and inadequate sanitation and hygiene, while 1.8 million people die from diarrheal disease each year. The WHO estimates that 94% of these diarrheal disease cases are preventable through modifications to the environment, including access to safe water.[1] Simple techniques for treating water at home, such as chlorination, filters, and solar disinfection, and for storing it in safe containers could save a huge number of lives each year.[2] Reducing deaths from waterborne diseases is a major public health goal in developing countries.
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 addition of inorganic coagulants such as aluminum sulfate (or alum) or iron (III) salts such as iron(III) chloride cause several simultaneous chemical and physical interactions on and among the particles. Within seconds, negative charges on the particles are neutralized by inorganic coagulants. Also within seconds, metal hydroxide precipitates of the iron and aluminium ions begin to form. These precipitates combine into larger particles under natural processes such as Brownian motion and through induced mixing which is sometimes referred to as flocculation. Amorphous metal hydroxides are known as "floc". Large, amorphous aluminum and iron (III) hydroxides adsorb and enmesh particles in suspension and facilitate the removal of particles by subsequent processes of sedimentation and filtration.[6]:8.2–8.3
We all know that dehydration can be dangerous, leading to dizziness, seizures, and death, but drinking too much water can be just as bad. In 2002, 28-year-old runner Cynthia Lucero collapsed midway through the Boston Marathon. Rushed to a hospital, she fell into a coma and died. In the aftermath it emerged that she had drunk large amounts along the run. The excess liquid in her system induced a syndrome called exercise-associated hyponatremia (EAH), in which an imbalance in the body's sodium levels creates a dangerous swelling of the brain.
In recent years, energy consumption has dropped to around 3 kWh/m3, with the development of more efficient energy recovery devices and improved membrane materials. According to the International Desalination Association, for 2011, reverse osmosis was used in 66% of installed desalination capacity (0.0445 of 0.0674 km³/day), and nearly all new plants.[19] Other plants mainly use thermal distillation methods: multiple-effect distillation and multi-stage flash.

These tablets essentially use chlorination as their method of purification. Sodium chlorite generate chlorine dioxide giving it the ability to treat water. Chlorination, as most know, is a common method of disinfecting water, and is commonly used by municipalities world-wide for this purpose. Chlorine destroys bacteria by destroying the cell walls of the bacterium/virus, killing the organism. Fortunately, when we drink chlorinated water, our digestive system quickly neutralizes the chlorine. So chlorine concentrations along the gastrointestinal tract are, in all likelihood, too low to cause damage. The tablets are wrapped in a metallic foil which makes it easy to store and there are no concerns of a glass bottle breaking. This is one of our favorite items to carry as a backup to our water filtration system.
The process of distilling seawater into drinking water has been used by the Ancient Greeks since about 200 AD (Wikipedia). Many cultures throughout history have used distillation as an effective method of ensuring potable water. Although the materials used in the distillation process have changed over time, the science has remained the same, proving that distillation is a purification method that has stood the test of time.
You do not want to wait until you are thirsty to begin gathering water, as the urge to drink directly from the contaminated source can become unbearable. Due to the negative effects of drinking water contaminated with Giardia and other bacteria/viruses, this is a bad idea. Becoming sick from drinking bad water, will further dehydrate you, worsening your situation.
A subcategory of sedimentation is the removal of particulates by entrapment in a layer of suspended floc as the water is forced upward. The major advantage of floc blanket clarifiers is that they occupy a smaller footprint than conventional sedimentation. Disadvantages are that particle removal efficiency can be highly variable depending on changes in influent water quality and influent water flow rate.[7]:835–6
As with any other filter type water purification method, careful attention has to be taken to pathogen/virus and chemicals size. During hurricane Katrina a lot of the water was contaminated with petroleum based chemicals from flooded cars. What is removed from the water is dependent on the filter pore size. However, it is difficult to beat the lightweight option that water purification straws and bottles provide for most situations.