This is the tricky part.

Start by feeding the wire through the connector on the back, give yourself enough slack to work with. Take your wire blade connectors and attach two to the white and black wires on the plug, and two to one end of the lamp cord. (I changed lamp cord to this higher quality one I had lying around)

Connect the black wire(Hot) to the brass screw, connect the white wire(Neutral) to the silver screw. Green wire goes to the green screw. Didn't take pictures of this part, but the included picture shows the basic idea, use the blade connectors to connect the wires to the outlet.

Next bring the other end of the lamp wire up through the 1/8 inch tube and out the top. Connect the black to brass, and white to silver. Don't need blades here, you should have enough room.

Lastly make sure it all fits inside of your box. I did my wiring to fit with the shape of the outlet/curve of the box. You may need to re-position some cables to get it all in there snug. Then test to make sure the wiring works before you seal it up.