Test your chemicals. A chemically imbalanced pool can prove to be corrosive to the liner, ladder, and other equipment. At least once a week, conduct a test for adequate pH levels, calcium hardness, and total alkalinity, and adjust accordingly. For an accurate test reading, obtain your water test strip sample from a submerged depth at elbow's length.
Shock-treat when necessary. This is typically done once a week but additionally after stormy weather conditions, or if you notice that the water is murky and slimy. Ask your local pool professional for the correct amount of treatment based on your pool; this adds sanitizers to your pool to break down contaminants. It is recommended that you do this after daylight hours, so the sunlight does not affect the chlorine.
Check your water levels. On average, your pool will lose a quarter of an inch of water every day. Sun exposure, temperature, and weather conditions can all affect the rate of water loss. Ideally, check levels at least once a week. Keeping your pool full is not just a matter of aesthetics -- it prevents components of your circulation system from being damaged. Consider an automatic pool water leveler, which takes the work out of it for you.
Skim the surface for debris. This should be done every day using a hand skimmer. If not, floating debris such as leaves, pollen, and bugs will sink to the bottom; this makes it more of a chore to clean and will put more strain on your circulation system. Additionally, clean your strainer basket.
Do a deep-clean. Once a week, vacuum the pool bottom for sunken debris. When the surface is clear, scrub the lining walls or tile to prevent buildup of algae. Depending on the lining material, use a soft brush (for fiberglass tile) or a stiff brush (for more stubborn stains).
Clean your filter. Depending on the type you have (cartridge, sand, etc.), the maintenance procedures and frequency of cleaning will differ (although an annual cleaning is recommended for all) -- consult your manufacturer's instructions. Be sure not to overclean it, as that will hamper its efficiency.
Watch for leaks. A significant consistent decrease in water levels could be the sign of a leak in your pool. For this, try the bucket test: Fill a bucket two-thirds-full of water and mark the level on the inside of the bucket with a pen. Immerse the bucket in water (if possible, on the steps of the pool or someplace it will not tip over) and mark the water levels on the outside of the bucket as well. After 24 hours, check the bucket. If the water levels decrease equally on the inside and outside of the bucket, it is likely typical evaporation. If the water levels decrease significantly more on the outside of the bucket, and not the inside, it is likely a leak and will require a call to your pool professional.
Cover your pool. When not in use, secure your pool with a cover. While there are several types to choose from, there are some that transfer heat to your pool water.
For more detailed questions, ask your local pool and spa professional.