These travishers, unlike most on the market, operate via a slightly curved sole which gives depth-of-cut control while the tool is in use. There is no fussing with the blade to get the depth set, leaving you with only one possible shaving thickness. Sharpening is also easier because the back of the blade is concave to make removing the burr faster, plus the blade has no tangs to get in the way when sharpening the bevel. The handles are designed for chairmkers and the curve of the blade closely matches the curves in a Windsor chair seat, leaving a smoother surface.
Use: In my shop, travishers are an intermediate tool in the seat carving process between initial shaping with an inshave and fine tuning the surface with a card scraper. Travishers remove the gross irregularities and they do it in a hurry; they are the jack plane of seat carving. That said, the body mechanics involved in using a travisher are somewhat counter-intuitive and can take some getting used to.
As with most edge tools, practicing NOT cutting is the best way to learn to use a travisher correctly. Hold the travisher in two hands, thumbs resting on the flat pads on either side of the throat, with the blade facing away from you (travishers are usually pushed). Put the travisher onto the work, then roll your wrists up and away from you until the blade is no longer in contact and the sole of the travisher is all that contacts the work (see photo). Now push the tool, trying to keep the blade from cutting. As uncomfortable as this may seem, this is where you should start each and every cut. Once you get the feel of not cutting, straighten your wrists slightly and the blade will come in contact with the work. Straighten them more for a heavy cut, less for a light cut. End the cut by rolling your wrists away from you to bring blade out of the cut; it's awkward, but rolling your wrists down will make the tool cut deeper before exiting the cut.
Blade Adjustment: As I already mentioned, these travishers are meant to be used in a way that gives you control over the depth of cut as you are using the tool. However, if you need to increase the blade exposure, inserting pieces of paper between the blade and the body will raise the blade; evenly scraping the sole will have a similar and more permanent effect. Carefully filing the shoulders which the blade seats on will lower the blade. It doesn't take much; one thickness of paper will have a noticeable effect.
Sharpening: Sharpening most tools is the same basic process: you sharpen the bevel with a coarse enough stone to be expedient, work up the grits to polish the surface and make a longer lasting edge, then remove any burr you've created by working it back and forth with your finest stone until it breaks off, leaving a crisp edge. There are many ways to do this, most of which work. Here are some thoughts:
The Bevel: A deburring wheel called a Beartex wheel (from MSC or Highland Hardware), followed by a hard felt or leather buffing wheel, is a quick way to sharpen the bevel. The Beartex is like a very aggressive buffing wheel and the tool can overheat or the edge be rounded over in a hurry, so it takes a little getting used to. Putting your wheel on a homemade threaded-rod mandrel, chucking it in a variable speed lathe and reducing the speed could solve this problem.
A safer method would be to screw the blade bevel-up to a wooden form and use some kind of slip (diamond, Japanese waterstone...) An old Japanese bench stone, the face rounded with a rasp, gives plenty of room for the hands if you plan on a lot of sharpening. The bevel can then be polished on a felt or leather wheel by skewing the blade on the wheel to give maximum surface contact. Start with the heel of the bevel contacting the wheel (to give you a frame of reference), then move the blade across the wheel towards the edge until you see a very slight feathering of the polishing compound curling up off the edge. This indicates that you are right on the edge. A heavy curl indicates you have tipped the blade too far, changing the shape of the bevel and blunting the edge.
The Back: The back of the blade must be kept flat. If the back is rounded over or made convex, however slightly, the tool will not cut, so only sharpening stones should come in contact with the back. No strops and definitely no buffing wheels. The back comes flattened and polished, so, unless you run the tool into a nail, your finest grit stone should be enough to remove the burr after sharpening from the bevel.
If the Beartex wheel gets away from you and grinding the bevel is the only option, a small grinding burr chucked into an electric drill should do the trick.