Wow, seems like everyone has a little bit of a different technique from the next. For what it's worth, this is how I cleaned my former car, a black audi a4. The audi paint was so soft that I swear it would spiderweb if you even looked at it. I haven't had a chance to wash the s2000 yet as I just got it and the weather has been crappy...but here goes:

1. Start off with 2 wash mits, a bucket of soap/water, and a bucket of regular water.
2. Spray down car. With wash mitt number one, I go around and do the bottom 1/4 of the car. Anything from the door trim down, front lip, rear lip, etc.. These are usually the most dirty/grimey parts of the car. No circular motion, only back and forth mimicking the wind flow. Light pressure obviously.
3. Making sure to rinse mitt in the clean water bucket after each side of the car, then i'd go on to the wheels, tires, and the exhaust tips.
4. After this is all done, dump out the rinse water, re-fill the bucket. and put mitt #1 to the side. If the car is particularly dirty, I might re-fill the soap/water bucket also. I also do a quick rinse of the lower 1/4 of the car, wheels, and tires so the soap doesn't dry up on the car.
5. Take mitt number two, and do the other 3/4's of the car.
6. Start on the roof, and work my way down, rinsing the wash mitt in my rinse bucket between washing each side of the car.
7. Rinse whole car, dry with absorber.

Now this may be pretty extreme for most, and honestly, it probably is if your car's paint is very soft and/or a dark colored car. I was able to do the whole car in about 35-40 minutes. But the results were worth it. Swirlmarks/spiderwebbing was kept to an absolute minimum, and people would always comment on how the paint on my car looked brand new.