Wash with a synthetic sponge. Real sponges can still have a tiny bit of sand or shell in them and scratch the surface. I use one for the car and another for the wheels.
For drying, I use the water blade on all the flat surfaces of the car, and "The Absorber" for everything else.
If you're going to use a towel, make sure it's 100% cotton and made in the USA. Fieldcrest or Canon brands are good. Stuff made outside of the USA can still have some synthetic stuff in them, even though they say 100% cotton. That synthetic stuff can put small scratches on the car.
And don't use dish washing soap on the car. It'll strip all the wax off the surface. Use a soap made for cars, like Meguiar's.