Though turtles generally aren't as sensitive to water quality issues as fish, turtle tanks should be treated much like fish tanks. As waste products in the tank break down, ammonia is formed, which is potentially toxic and can be irritating to your turtles even at low levels. As a tank becomes established, beneficial bacteria grow in the tank and filters; some bacteria break down ammonia into nitrites (also toxic) which is converted by other bacteria into less harmful nitrates (less toxic - these are then controlled by water changes). Before this "nitrogen cycle" becomes established, or if it is upset in an older tank, levels of harmful by-products or the bacteria that use them can spike, causing problems such as cloudy water. For more on this process see The Nitrogen Cycle on the Freshwater Aquariums site at About.com.
In a nutshell, maintaining water quality depends on removing wastes as well as establishing colonies of healthy bacteria that will break down waste products. There are several ways to make maintaining high water quality easier.
Measuring Water Quality
Pet stores carry test kits for ammonia, nitrates and nitrites. Monitoring the levels of these can help you catch conditions in the tank that can be irritating or harmful for your turtles. Check with the pet store and follow the directions included with the kits (the instructions will also have information on safe and dangerous levels of each chemical). If the levels of ammonia, nitrates, or nitrites are too hight, do a complete water change. If you find your levels are moderate or creeping up, do more frequent partial water changes (or a complete change).
The pH (a measure of acidity) is not as critical as the waste products, but measuring pH is also a good idea. Generally red eared sliders are pretty tolerant of small pH changes, but picking up on the changes can alert you to the fact that the chemistry in your turtle's water is changing. The pH should be in the range of 6-8 for red eared sliders. Products can be found at the pet store that can be used to safely lower or raise the pH if necessary.
What about Chlorine in the Water?
There are conflicting opinion on whether tap water should be dechlorinated for turtles. Turtles may not be as sensitive to chlorine as fish or amphibians, but it can still be irritating to them (especially their eyes). It is also important to consider that chlorinated water may destroy the beneficial bacteria in the tank, affecting the nitrogen cycle and breakdown of waste products. It is therefore ideal to dechlorinate the water (the easiest way is to use water conditioners available at pet stores. Some cities use chloramine in addition to chlorine to treat the drinking water; if this is the case where you live, find a water conditioner that is labelled to remove chlorine, chloramine and ammonia (a by-product of the deactivation of chloramine). Chlorine will dissipate from water after about 24 hours, but chloramine does not.
Remember, when you are changing water, cleaning filters or other turtle tank accessories, and handling your turtles, be aware of the risks of salmonella and take appropriate precautions.