The water spots you see on your car's paint after you wash it are caused by minerals left behind from beads of water that have since evaporated. These mineral deposits are on the surface of the paint and can be easily removed by washing your car again and drying it with a soft dry cloth or a damp chamois before the beads of water can evaporate.
The best way to keep your car spot free is to prevent the spots in the first place. You can do this by using water that has little or no minerals to leave behind. Well water is generally the worst water to use for washing your car, sometimes even a thorough drying will not prevent water spots or streaks. City or town water from a reservoir is usually a little better but will generally leave spots as well. In either case a rinse with distilled water after washing will prevent the spots.
You can buy distilled water by the gallon at most grocery stores. After washing and rinsing your car, wipe it down with a chamois cloth to remove any excess water. Using a clean chamois and a bucket filled with a gallon of distilled water dampen the chamois in the bucket and wipe your car down again. Squeeze out the chamois frequently letting the water fall on the ground and replenish with distilled water. When the car dries it will be spot free.
A quality car wash will use highly filtered and treated water during the rinse to prevent spotting. If you use a self serve car wash always use the spot-free rinse after you wash.
If you cannot remove the water spots by washing the car then you will need to buff out the paint. There are several products on the market to help with stubborn water spots. A rubbing compound or a mildly abrasive chamois may do the trick. These products are abrasive and if not used properly can damage a car's finish. Be sure to follow the instructions very carefully with any product you choose to avoid serious and permanent damage.
Once your paint is free of spots you should apply a good quality automotive wax to protect the paint. A good wax not only brings out the color and shine in your car's finish but that shine has a practical purpose as well. The surface shines because it is very smooth and a smooth surface will cause the water to run off where it can and prevent residual minerals from grabbing hold. The wax acts as a nonstick surface between your paint and the minerals for fast and easy cleaning between waxing.