There is a simple "picture schematic" in the images for the page. I used an arduino nano v3. It doesn't matter which axis go to which analog pins or which buttons go to which digital pins, you can manage which channel is which axis in vjoyserialfeeder and each game will need to be set up with customized config anyway.

The pulldown resistors are 10k, the joysticks are 10k. The joystick tactile buttons are not included in the build. 5v runs from the arduino to the rails on the breadboard, so does ground. The joysticks just plug directly to the analog pins. The power runs from the rails to the tactile buttons on the breadboards, and from the buttons the wire runs to the pins on the arduino. A pulldown resistor is placed between the arduino pins and ground. This means that the sketch will read high as press. 

I have found that the small buttons are difficult to press in the trigger positions, because your fingers pull at a different angle. Your thumb will easily interact with the buttons, but you are only holding the board with your fingers and palms, so in order to make it easy and smooth to press the buttons on the bottom (your triggers!) I mounted a small block between the buttons and mounted some broken propellers to suspend over the buttons. Then you have a nice surface area to interact with and can easily pull in any direction to press the buttons. If you don't have propellers then you can use plastic knives, or some other flexible yet stable plastic. 

The setup for vjoyserialfeeder is pretty easy. I have also uploaded my configuration json, but if your pins are not in the same order as mine, then your axis and buttons will not have the same number order. This doesn't matter though, because you will need to map all of the controls in each game anyway, and mostly you just select the control and press the button or deflect the stick you want, so it's really fine. You will need to calibrate each of your axis, and while using a breadboard you may need to calibrate frequently. If it is soldered together, calibration should be very stable. Don't forget to hit save after you calibrate.

make sure the correct drivers for the specific arduino you have are installed, most of the arduino boards I have use the "ch340" , there is a sparkfun tutorial for the driver installation. You will need these drivers if the arduino appears on device manager as a serial usb device instead of in the com-ports as "ch340 device". -- run the "configure vjoy" app and ensure you have 8 axis and 12 buttons in the profile you set up, none of the other settings should be changed. -- make sure you have the correct comport selected in vjoyserialfeeder, you can check in device manager to see which one the gamepad is. -- once vjoyserialfeeder shows the controller and all of the controls respond, you can verify in "set up usb game controllers" that everything is feeding through vjoy correctly, just check the properties of the vjoy device. -- you should not need to restart your computer after a basic setup, but if you just installed vjoy, or the ch340 drivers, or you just reconfigured vjoy, you may need to. -- presently the Starmade joystick configuration is whacky, you will need to reset your configuration every time you go to the menu, as well as every time you load the game. This can be frustrating as if you need to simply invert an axis, you may need to reset all of your controls to do so, however starmade is very worth the effort, as my courses are just so darn well made.!