Fill up a standard water or soda bottle with water from the tap, or whatever other water source you are using.
Cover the opening of the second water bottle with a coffee filter. The coffee filter is going to remove larger objects from the water (such as specs of dirt and other debris), however, smaller organisms can still make it through the filter. To attach the filter to the second water bottle securely you may want to use a rubber band.
Pour the water from the first water bottle slowly into the second bottle. Pouring the water too quickly can cause damage to the filter and even break it.
Drop a water purification tablet into the water and let it dissolve completely. This tablet is going to kill off any germs that may still be in the water. If you do not have any purification tables you can pour 1/8 teaspoon of bleach into a gallon water bottle and shake thoroughly. Because the bleach amount is small you won't be able to taste it (nor is it dangerous) but it is going to kill the germs. Allow the bleach to sit in the water for at least 30 minutes before drinking.