This is the updated wiring for this arrangement, with a 2-wire cable added between the fan/light and switches. The white wire is no longer used for hot and the source neutral is run through to the switch box to satisfy the 2011 NEC requirement of a neutral wire in all switch boxes. All other wiring is the same as above.
The hot wire to the fan in a fan/light kit will usually be black and the light wire will be blue. The white wire is usually the neutral which is always connected directly to the source neutral, either at the source or through a splice in the switch box. The white wire may also be used to carry current when necessary.
The white wire is wrapped with black tape to identify it as hot. The black wire connects the fan to the speed controller. The red wire connects the light to the dimmer.
Here the source is at the fan/light and a switch loop runs to the wall switch. The source is wired directly to the fan and spliced through to the switch. With this arrangement the light is controlled with the switch and the fan is hardwired for pull-chain control.