When the water you're hoping to drink might be riddled with parasites or bacteria particles, you can't afford to skimp on water purification. In the very circumstances that put you in contact with questionable water (being in the wilderness, surviving or recovering from a disaster, or living in a part of the world where water isn't purified for you) the last thing you want to do is to get sick.

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Boiling
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Place the water you wish to purify into a pot. Place the pot on the stove and turn the stove on to high. When water boils, any bacteria that may have been living in it will be killed, thus reducing your chance of getting sick when you drink the water.[1]

If you are in the wilderness when you need to purify your water, build a fire to boil your pot on. If you do not have pot, you can use any container that is fire-proof.

Bring the water to a rolling boil. When bubbles begin to appear, it means that the water is starting to boil, but continue heating until the water goes into a hard, rolling boil, then start timing. Continue to boil the water for 5-10 minutes plus 1 minute for every 300m above sea level, up to around 5500m where boiling becomes ineffective, to have the most effect upon any bacteria and other micro-organisms.[2]

Boiling water for 1 to 5 minutes will purify it sufficiently. [3] It will kill off the vast majority of organisms living in the water. It also removes some chemicals by vaporizing them. However, be aware that boiling the water will not remove solids, metals, or minerals. Also be aware that the boiling point of water decreases with altitude, so you will not get the same purification effect on a mountain top as you would on a coastal plain. You can boil the water longer or use a pressure cooker to offset the lower temperature.

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Remove the pot from the heat. Use caution when handling the pot and water as they are, as you may have guessed, very hot.
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Let the water sit and settle. You do not need to do this if you are boiling water that came from a tap and you feel sure that there are no solid items, minerals, or metals in the water. If you let the water settle, any dense items in the water will sink to the bottom naturally, allowing you to drink the pure water from the top.[4]

Creating a Purifying System in the Wilderness

Form a cone out of a strip of bark. Birch bark, or a bark similar to it, is best for creating this filtering system because it is flexible but will keep its shape. Keep in mind that this method will not fully purify the water, but it will reduce the amount of microbes in the water. This method should only be used in extreme emergencies.[5]

If you are having a hard time keeping your bark in the shape of a cone, you could try tying a piece of rope or a durable type of grass around it to keep its shape.

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Layer the cone. Wildwood Survival suggests layering the cone with sand, charcoal, grass, and gravel (or small rocks.) Charcoal is especially good for removing bacteria. If you had fire, crush up some of the burnt pieces of wood.[6]
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Pour the water through the cone and into a container. Do this several times to increase the amount of purification that occurs. Again, this method does not guarantee purification, but it will remove a good deal of the contaminants in the water.

Making a Solar Still

If you are in an area with a lot of sun, this method may work for you.