It's actually pretty simple, I'm happy to say: You don't even need to open the door that covers the light, and it's designed to be done in just a few movements. The description below is long because it's detailed, but after doing it a couple of times the motions should come together. Oh, and I have no idea what all these things should be called...
Looking at the front of the machine from left to right, you'll see the door, a wider gap with a small rounded metal sticking out a bit (this needs to be at the top when you thread), the edge of a plate which is wider at the bottom, a narrower gap with the edge of a narrow wheel at the top, and next to that the wide edge of a plastic wheel. Above the plastic wheel, on top of the machine, there's a metal thing with what looks like a watch battery lying on it, and a curled hook standing up.
You thread the machine in reverse order from the description above, from right to left.
Hold the thread between your hands with about 2 inches showing (sort of like dental floss) under the hook part of the metal thing on top. Pull the thread just slightly towards you, then up and under the hook part. Pull out about 18 more inches.
After this point, 2 things are very important: Keeping constant tension on the thread, and holding it within 1/2 to 1 inch of the machine. You keep the tension by planting a finger from your right hand on it, very close to the edge of the narrow gap,and keeping it firmly there the entire time. Use your other hand to guide the thread.
The next chunk, between the metal gizmo on top and the needle assembly on the bottom, will eventually become 1 fairly fluid movement.
Bring the thread straight down the narrow gap in the body of the machine, so that it slips between the two wheels, and all the way down the narrow gap. (It should not be between the narrow wheel and the plate - if it is, pull it out from the top and try again.)
With the thread at the bottom of the narrow gap, tug slightly to the left and the thread will slide behind the wider part of the metal plate-edge. Pull the thread all the way up, then all the way to the back of the narrow gap, then to the left and to the front again, and the moving small round metal bit is threaded.
Pull the thread all the way down to the bottom of the wide gap, so it's to the left of the wider plate. There's a bit of metal across the bottom of the gap; push the thread against it and slightly to the right, and it should slip behind the bit of metal. (That's the end of the '1 fairly fluid movement' part.)
Using both hands now, hold the thread floss-style again, very close to the needle assembly below the machine. Just at the top of the needle there's sort of a nut around the assembly, with a stiff wire below it; push the floss-like piece of thread between the nut and the wire, and pull the left end back and down a bit - and you're done!