Here is the way I was taught years ago to sharpen a hand scraper.
The first step is to put the scraper in a vise and using a fine file, file the edge perfectly perpendicular to the sides. Only a couple of strokes should be necessary and this is normally only done on a brand new scraper or one in bad shape. Next, using a fine oil stone, hold the scraper flat on the stone and remove any burr and smooth the sides near the edge. Holding the scraper straight up on edge (90 degrees to the stone), hone the edge and then lightly remove the burr. There is a tendency for scrapers to dig into a soft waterstone so I use an inexpensive fine oil stone. 400 Wet & Dry sandpaper lubricated with light oil or WD40 would work fine.
Burnishing is the next step. After filing and being sure the edge is flat and 90 degrees to the sides, put the scraper flat down on, and slightly back (1/4") from the edge of your bench. Run your burnisher along the flat side of the scraper pressing it so the burnisher is tight at the edge. This starts causing the edge corner to extend. This is a step that burnisher jigs can not do. Now put the scraper in your vise extending up about an inch. With your burnisher, run it along the edge at 90 degrees from the sides. Take 2 or three not too heavy strokes. This causes the corner raised in the first step to be bent toward the sides of the scraper. Then tip your burnisher up slightly (10-15 degrees--really makes no difference) and take two continuous, firm strokes on each edge. That's it.
You will have to try scraping at various angles to find the "sweet spot." As the scraper becomes dull, go through the same three burnishing steps as above. You can burnish 10-20 times before stoning or filing is again required. It takes less time than changing sandpaper in a sander.
I greatly favor a real burnisher for two reasons. First, it is really hard metal. Second, it it highly polished. Both of these attributes mean that there is little chance of galling (or tearing metal from) the scraper edge. Galling makes for less than a smooth cut. The smoother the burnisher, the smoother the burr. Screwdriver shafts may or may not be hard enough and the chrome plating will eventually deteriorate. Drill bits are also variable in hardness. Using a valve stem from a car engine that has been highly polished is an alternative but, why not just get a burnisher?
Finally, you can control the aggressiveness of the scraper by the way you file/stone it and how you use the burnisher to make the burr. Stoneing with a fine stone after filing and then using lighter pressure on your burnisher will give you a less aggressive but finer cutting burr and a smoother finish. I have a thicker scraper that I sharpen to an aggressive cutting burr that I use for initial work (ie: ripple removal after jointing/planing) and then a set of thinner scrapers that I put a finer edge on for finish smoothing and cutting down and smoothing varnish finishes.
Finally, to prevent frustration, scrapers work best on hard woods. Using them on pine is generally unsuccessful.
For an excellent description with pictures get Bob Flexner's "Understanding Wood Finishing."
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