The black wire is splice to the output on the speed controller and to the black, fan wire at the other end. The red wire is spliced to the output on the dimmer and to the blue, light wire at the other end. The neutral from the source is spliced in the switch box with the white wire, and to the neutral wire on the ceiling fixture at the other end.
To wire an exhaust fan to a wall switch, use this diagram. These fans usually come with a small electrical connection box welded to the side of the housing. There will be a cover on the connection box that fastens with a small screw. Open it, pop the plug out of one of the wire holes and thread a wire clamp into it.
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.
To wire a 3-way switch circuit that controls both the fan and the light, use this diagram. As with all 3-way circuits, the common on one switch is connected to the hot source wire from the circuit. The common on the second 3-way switch is connected to the hot wires on the fan/light.