At each corner of the baseboard, install a standoff using a single screw with a plain washer. This elevates the board to make room for the wires and connections underneath.
Solder any necessary wires to all the electronic components (follow the data sheets and the below wiring diagram). Using heat shrink tubing may also be a good idea to prevent shorts. Next, mount all the of the components onto the baseboard, following the image below. Use zip ties, screws, washers, nuts and spacers wherever needed. Connect the air flow between components using appropriate tubing.
Now that all the components are in place, they need to be connected to each other, following the wiring diagram below. A good place to start is by connecting all the components to power. Use red and black wires to represent voltage supply and common (ground), respectively. It may be helpful to use a bus to manage the various power wires.
When connecting signal wires, be careful not to mix up the Arduino's digital and analog pins (analog pins are prefaced by 'A'). Use the breadboard as an intermediate between the components and the Arduino to help keep all the wires organized. You can also connect 5 VDC and ground to the Arduino's Vin and GND pins, respectively, so that it remains powered even if the board is not connected to your computer via USB.
Before connecting the control board to power, make sure there are no short-circuits. If the board doesn't work properly at first, use a multi-meter to diagnose the problem and double-check your wiring. After connecting all the power plugs, make sure none of the components are getting too hot!