Find the boiler's terminal block, usually located on the burner toward the back, near the end that would be facing the wall. Click open the front panel and angle it upward at 90 degrees, so that you can see the inside of the mechanism as well as the connections on the front case.
Connect the power cable to the main box. The power cable will be black and thicker than the other cords you see, split into three slimmer ends which should already be loosely connected to the front case. Tighten the bolts on that connection, using pliers. Then slide the wire under one of the center clamps and into the cable grommet farthest on the right. Use a small Phillips screwdriver to tighten the cable clamp, after you've secured the wire through.
Connect the remaining thermostat capillary wires, according to their colored code. Each wire end should have a color corresponding to that of an entrance. Each wire needs to pass through a cable grommet, and they should be clamped down individually. No wire should be loose without a clamp.
Check the cables to make sure everything is connected and there are no loose ends. Once every wire is attached, be sure they are each slack enough to handle the shutting of the apparatus. If drawn too tight, the cables could pull out, leading to an electrical short. Double-check everything mentioned in this step before turning on the power.