The source hot is spliced to the red wire which is connected to the bottom terminals on the switch at the other end. The black wire is connected to the top terminal on the switch which runs power back to the fan where it is spliced to both the black and blue fan wires.
In this arrangement with 2 switches in one box, the bottom terminals are connected to pigtails spliced to the source. The top switch terminals connect to the black wires running to the light fixtures. The source neutral and ground wires are spliced to run to each light box.
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.
This diagram is similar to the one above, but with the electrical source originating at the fixture. Three-wire cable runs from there to the controllers. The neutral wire from the source is spliced directly to the white wire on the fan/light. The hot source wire is spliced to the white on the 3-wire cable and then spliced to the input wires on both controllers at the other end.