To begin, you have to do the Singer badge.
This was attached by the two brass pins you can seen in the picture. They were driven through holes in the body of the sewing machine, and then just bent over on the inside. Very tricky to un-bend and release the badge. Also, when I removed it to prepare the body, I found a second badge in pristine condition right behind it! I wonder how often that happened? I'm sure you can guess which one I used.
I started with the shafts underneath the bed.
This went pretty quickly, except that I attached the bobbin shaft backwards (the front end toward the back). Didn't work very well that way. Much better when I placed it correctly.
Then I moved up to the throat of the machine. Not much had been taken off here, since I would have had to remove the unyielding Arm Shaft to take anything else out. But the Stitch Length Adjustment knob was very tricky to put back into place.
The other end of the shiny knob in the left photo is held by a sleeve (visible through the hole in the right picture) that controls the motion of the Rocker Arm that moves the feed dogs. As you can see, it's not a place where fingers can get into very well.
Next were all the goodies behind the Face Plate: Needle Rod and Presser Foot Rod, Presser Lifter and Thread Tension Control.
The rods went back into their clamps where the marked (when taking apart), and the cams and levers popped into place with a minimum of fuss.
Finally, the external pieces: Needle and Slide Plates, Presser Foot and Needle Clamp, and the cover plates.
With a few drops of sewing machine oil, the newly refinished sewing machine seemed to move just fine. But I found that it would not make a stitch. The Vibrating Shuttle would not catch the loop formed by the needle, and the thread would get tangled up and break. I tried adjusting the shuttle timing, as described in the manuals, but still could not get it right.
Finally Susan took a look, and exclaimed that the thread tension was waaaay too tight. I loosened it up to a reasonable level, and look, stitches!!! Also, in trying to use the bobbin winder to fill the long bobbins, I found that the ones that came with the sewing machine were not Singer bobbins (just a little bit too short). I found a supplier for real Singer bobbins on Amazon (what did we ever do before the internet?).
I ordered a suitable electric motor for it from EBay, and it quickly came -- just the motor, no foot controller or belt! So I borrowed a foot controller from another machine, and got a belt from a sewing machine repair store. Finally, I could "step on the gas", and watch as stitches merrily flowed from the refurbished machine.