Step 2: Clean, and begin putting it back together.
Start with the spring loaded gear at the bottom. The end of the spring is held between a screw head and a brass spacer. Don't over tighten it, you can collapse the spring.
Do you remember the tension? If not, you will have to wait until you get the pivot gear (Oddly shaped brass gear) and pinion gears assembled.
What you are looking for, at full extension of the micrometer (The largest opening) is a spring that is tensioned, but not so that the coils are overlapping. You can bring it up to that point, but if you do, back it off a few teeth. Hold it there with the backing plate on with a small screwdriver.
The purpose of this spring is to keep tension on all of the teeth, all the time. This is because nobody can maintain perfect 1/100,000" meshing of all of the teeth on all of the gears. A simple spring keeps everything tight and ensures an accurate instrument, all of the time. Neat, huh?
I did not do much cleaning of the internal components. They are generally pretty clean. But if you want, you can use a small wire brush to clean the teeth, but don't go nuts. The teeth are tiny and very delicate.