The primary ingredient for washing your car is water, preferably "soft" water. In many areas of the country, the local water supply is "hard" containing many minerals. The little rings or film that is left on your car's surface after it has dried is the result of "hard" water.
Since you usually can't change the local water supply, the next best thing is to dry the surface before it has a chance to dry itself.
Into the water you usually add soap. Don't use detergents or common, coarse soaps. Your car's paint never truly dries out, but is always evaporating residual oils into the air. Harsh detergents will remove these oils, causing the paint to dry faster than normal. Instead use warm water and a non-detergent soap made especially for waxed surfaces or a liquid soap made for waxed surfaces or a liquid soap made for washing dishes by hand. Other products that can be used on painted surfaces include baking soda or plain soda water for stubborn dirt.
Wash the car completely, starting at the top, and rinse it completely clean. Abrasive grit should be loaded off under water pressure; scrubbing grit off will scratch the finish. The best washing tool is a sponge, cleaning mitt or soft towel. Whichever you choose, replace it often as each tends to absorb grease and dirt.
Other ways to get a better wash include:
One of the best implements to dry your car is a turkish towel or an old, soft bath towel. Anything with a deep nap will hold any dirt in suspension and not grind it into the paint.
Harder cloths will only grind the grit into the paint making more scratches. Always start drying at the top, followed by the hood and trunk and sides. You'll find there's always more dirt near the rocker panels and wheelwells which will wind up on the rest of the car if you dry these areas first.