You're supposed to sheet off as much water as possible with the hose. Take whatever pistol may be on the end, and let the water run out in sheets over the paint. It really helps if the surface has wax/sealant (reason why it's easier to wash a well taken car of car).
If you have time, use a leaf blower. Electric is much better since the gas power ones will sometimes spit out traces of oil (or so I've heard). We just use an electric one on the whole car, but mainly focus around the wheels, mirrors, handles, and and badges or areas that might hold water.
Chamois are usually avoided because they don't have much "nap" to them. If, for whatever reason, any dirt gets caught in there, it'll be dragged across the paint.
Generally, microfiber towels are used. You're supposed to blot, to minimize micro marring from dragging the towel around. I usually do a mixture of both, though drag it if I'm about to detail it (to save time). Any micro marring induced will be taken care of during the detail.