Do not use dish soap. Spend the 5 bucks for automotive soap. You should also pick up a lambswool wash mitt for 6 dollars. Don't use brushes, old t-shirts, bath towels, or microfiber while cleaning the car unless you're dealing with non-painted parts.
When washing, use a two bucket system. Fill one with soap and water, the other with clean water. Dip the wash mitt into the soap, wash a panel of the car, and then rinse it off in the clean water bucket before going back for more soap. Don't let the mitt touch the bottom of either bucket. Change the clean water bucket when it starts looking dirty. Also, wash the car from top to bottom and don't use a high pressure nozzle. The "fan" setting on most garden hose nozzles works well. If you haven't washed the car for a while, washing it twice wouldn't be a bad idea.
Dry the car with several clean microfiber towels. If you have cotton towels, you can use them, but just lay them flat on a panel and push down to absorb the water. Don't wipe the surface of the car with bath towels or t-shirts. Follow up with microfiber. That's all there really is too it. Then you can commence claying!