The idea behind hand scraping is pretty simple.
Take a piece of metal:
Spread pigment across something that you already know is flat:
Rub the piece of metal against the inked surface plate. The highest points will end up marked:
Take a scraper, which is basically a long chisel, and scrape off the bits that are colored. With a nice sharp scraper and some skill, you can remove very thin layers of metal, easily down to 1/10000 of an inch, and 1/100000 if you're good.
This piece took me at least 10 cycles to get reasonably flat. (Note that it is flat, not smooth. Hand scraping always leaves channels between the high points, but that's usually a very good thing. If you have two pieces of metal rubbing against each other, you want room for the oil.) It could have used several more cycles, but I wanted to continue with doing the other side, getting that parallel with the first, and then doing one of the edge at a precise right angle. By the end of the second day I was getting halfway decent at it, and the final surface I scraped is pretty darned nice.
If you've been paying attention, you're probably asking where the reference surface plate comes from in the first place. This is the really cool thing. Using these techniques, you can make a surface plate without any precision references at all. Take 3 rough castings, call them A, B and C. Ink up A, rub B against it and scrape off the high points. Now ink B up and rub/scrape C. Then C and A. Repeat a whole bunch. All 3 will converge on perfect planes, because that is the only shape that can nest perfectly across 3 objects. (If you only used two, they could become matching convex/concave spheres.) The same trick works for making right angles, once you have a surface plate to work with.
It takes a lot of effort and even more patience. This is not something to do if you're easily frustrated. One wrong scrape can add hours of work. The marking process is very exacting -- the differences you're looking at are so tiny that it's very easy to mess things up without realizing it. A speck of dust in the ink will lift up your workpiece and change the markings. Directly holding your workpiece as you walk over to the surface plate can warm it up enough to cause it to warp slightly. Everything has to be done deliberately and carefully for hours on end.
I loved it. It's all a contest against yourself, to see just how patient and exacting you can be. I love knowing that I can make precision out of precisionlessness. This is to machining what processor architecture and assembly language is to CS. You might never use it, but knowing how it works all the way down is still important. I think I just might get some (small!) unfinished cast iron surface plates and do the A-B-C trick, just to have done it. 3 of them at a square foot each would probably take me a day or two of actual labor, but it would be worth it.