Steel beats wood, stone beats steel...
In the course of whittling wood, especially harder woods like pear, box, and lignum vitae, it is not unusual for the edge of one's blade to become round, rubbish, and worthless. Don't throw it away! You must sharpen it! But how? With all that time taken to carefully select your perfect knife, equally you must find your ideal method of sharpening.
What is a sharp edge?
A nice maxim regarding edges: "A sharp edge is the intersection of two mirror polished surfaces".
We can think about this on a microscopic scale. When a blade is blunt, it is rounded over. When ground, it gets a sharp cross-section, but it has microscopically tiny jagged teeth along the edge. When used, these will bend over and stop the blade working well. The aim of using finer and finer sharpening stones is to make these teeth small, smaller, vanishing, then you have a nice glass-like edge. Ow. The angle of the edge determines how tough it will be, and only the very last part of the edge needs to be highly polished...
The usual way of sharpening is on a set of sharpening stones. If your blade is badly chipped (chips 1mm or bigger) or the sides of the bevel rusted, you may need to use a coarse stone (coarse=grinding), something like a few hundred grit. If you can't be bothered to buy this stone, you can clip some wet-and-dry paper of a similar grit to a perfectly flat surface - I use a granite pastry block from Sainsbury's.
After you've got the chips out and the sides are clean, you can move on to the medium stone (800-1200 grit, medium=sharpening), then the fine (3000+, fine=honing). I use a Japanese combination water-stone which is 1000 on one side and 6000 on the other. The last stage in sharpening a knife is to use a leather strop to buff it. This is simply a piece of leather nailed to a block of wood which polishes the cutting edge, and can be used at the end of each whittling session to prolong the life of the edge. It only takes on the order of a few minutes on each stone to get the blade sharp.
Once the edge of the blade is honed, it is usually sufficient to use just the fine stone and strop to maintain the edge, unless heavy work dings it out of shape.
Information abounds on the net regarding how to sharpen knives, much of it contradictory of course. These gents talk primarily from the point of view of kitchen knives but I find their explanations on the motion involved in sharpening to be helpful:
Some more technical info can be found here:
Fine Tools 1
Fine Tools 2
This is in contrast to one web-page that I came across that would have you believe sharpening a chisel takes 12 hours -- when would you get to use the thing? There are many techniques, and the only way to understand them is to try them out; ultimately, you will know that you are sharpening well because your blade will get sharp. Do not get discouraged! It takes a little trial and error.
There exist both oil-stones and Japanese water-stones. oil-stones last pretty much forever while water-stones eventually wear out. In my experience, water-stones are quicker and easier to use. Because of their fast action, I would especially recommend them if your knife is of very hard stainless steel, but then I would recommend them anyway. I use a 1000 and a 6000 grit water-stone and finish with a strop. The blade achieved is sharp enough to shave with (if you are a sailor and can take a rather tough shave). However, I also have oil-stones, including a very fine and old one purchased from Deptford market. For some reason, I like to sharpen certain tools on the water-stones, and certain on the oil-stones -- I've no idea why.
BTWC offers knife-sharpening services and instruction, in fact we always have.