Make sure you have an appropriate fuse and switch somewhere upstream of the transformer <insert "you can die from high voltage" comments here>. I can barely see the colors in the picture, but the blue wire on the transformer input is neutral and the brown is hot. In the US for home wiring that would correspond to white and black, respectively.
One side of each panel would then be connected to the neutral (white?) from the transformer output. The hot/common (black?) from the transformer would be split into four wires, and each wire would connect to the four "COM"s on the relay board. You would then take four separate black wires and connect them between the "NO" (normally open) on each relay to the second pad on the panel.
It looks like a digitalWrite(HIGH) to any of pins 0, 1, 2, or 3 on the Arduino then activates the respective relay. Be warned that pins 0 and 1 will flicker when you're uploading a program to the Arduino so you probably want to disconnect the shield whenever you upload a sketch. There are cheaper relay boards out there (example and tutorial) that would be less restrictive in that respect -- while you can't stack them right on the Arduino you have more flexibility in which pins to use.