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.
Run the cable through the clamp and tighten it down. Splice the cable wires to the fan wires using a pigtail splice and a wire nut. Connect the ground to the grounding terminal in the connection box and the ground wire from the fan, if there is one.
Here the exhaust fan is controlled by a timer instead of a switch. There should be two hot wires and a ground coming out of the timer casing, splice one of these to the hot source. Spice the second to the black, cable wire running to the fan. Splice the source neutral to the white cable wire and the ground to the ground wires. At the fan splice the wires, matching the colors of each.
In these cases, it should be wrapped with electrical tape to mark it as hot. The ground wires will be green and/or bare copper. The ground should be spliced with a short piece of wire and connected to each device and outlet box that has a grounding terminal. In these drawing the brass colored terminal represent the hot side of the device and the silver colored terminal represent the neutral. Ground wires and terminals are in green.