Very little of the water we use every day comes out of the ground completely pure. Some of the impurities are microscopic, but many are large enough to remove with a crude filtration system that you can make yourself using sand and rocks. It's important to remember that this filter does not render the water potable. Enjoy the experiment, noting how much clearer the water appears after passing through it, but don't drink any of the filtered water, because it may still contain pathogens. Wash your hands with soap after doing this experiment.
Use a knife to cut 10 centimeters (4 inches) off the bottom of a 2-liter plastic water bottle.
Remove the bottle cap. Attach a coffee filter to the outside of the bottle neck using an elastic band.
Cut 10 centimeters (4 inches) off the top of a second 2-liter plastic water bottle.
Turn the first bottle (the one with the coffee filter on it) upside down and insert it, neck first, into the second bottle. The top bottle is the filter and the lower bottle is the water collector. Trim the bottles if they do not fit snugly into each other. If preferred, a beaker can be used as a water collector.
Pour gravel into the bottle opening. The coffee filter should prevent it from falling through the bottle neck. Add coarse sand on top of the gravel. Tip fine sand on top of the coarse sand to create a layered effect.
Pour tap water through the filter to clean it. Hold the filter close to the tap or pouring spout and pour slowly so as not to disturb the sand.
Pour dirty water into the filter to test it. The water collected in the lower bottle should be filtered clear. Your filter is now complete.
TL;DR (Too Long; Didn't Read)
Use beach or play sand for the fine sand. Aquarium rocks are a good choice for the rocks. To make even cleaner water add a layer of carbon or charcoal on top of the fine sand.
Be careful when cutting the bottles, and get adult supervision if necessary.