Here's the next part on this set. Buffing is generally done with cloth wheels impregnated with some kind of fine abrasive. By going to finer & finer grits, you can go all the way to a mirror finish. Done right, so bright and clean that it actually is a mirror-smooth surface.
Warning note: In some ways, polishing on wheels can be more dangerous than grinding. A soft cloth wheel turning several thousand rpm can grab a piece out of your hands and throw it. I mean literally grab it and throw it. I've seen a wheel take a gold or silver ring out of a jeweler's hands and throw it hard enough to dent plywood. It can do the same thing with a blade. I've read one account of a maker who, trying to put that last little touch of brightness on a knife, had a wheel grab it, carry it through one rotation and throw it point-first into his thigh where it buried the six-inch blade all the way up to the guard. He damn near bled to death before help arrived.
Also, they throw out a lot of dust and abrasive particles and lint, so you'll need the lung protection here, too.
A buffer can be anything from a bench grinder with buffing instead of grinding wheels, to a dedicated buffer like the Baldor. A dedicated buffer can be expensive, but they're good. One of the good things about them is they generally have a much longer shaft on each side, which gives a lot more clearance around the motor; easier to work on long or odd-shaped pieces.
Two main types of buffing compound, greaseless and grease. Grease compounds are some type of grease or wax base with the abrasive mixed in. Greaseless are generally glue-based, something like hide glue, with the abrasive added. Grease-type compounds leave some traces on the surface, which will need to be cleaned off before going to the next step. Greaseless leave a cleaner surface behind. Most of the grease types will stay hard up till fairly hot temperatures, greaseless need to be kept refrigerated. Grease types you hold up against a spinning wheel and some rubs off, and often rubs off fairly quickly. Greaseless you hold against a wheel and the friction melts some; what adheres to the surface is given a minute or two to harden, and it often lasts longer. In my experience the greaseless are faster-cutting. Both are available in many grits, from coarse to extremely fine.
There are different kinds of wheels for this work. The most aggressive I know of are woven sisal fibers. They cut circles out of the fabric, stack several, put some fabric on each side and stitch them together. Good with coarse grease compounds for fast cutting.
The top of the line for wheels is felt. They come in soft to rock-hard firmness, and can be used with all types of compounds. The corners stay sharp and this makes them excellent for polishing right up to a line, say where the blade bevel meets the flat ricasso. These are also good for another thing, finishing an edge. If you need an edge finished as finely as possible, after sharpening use one of these wheels with a very fine compound to polish the edge; you may be amazed at the result.
All other wheels are some type of stitched cloth. For keeping a surface as flat as possible you'll have layers stacked up and glued together so you have a stiff wheel with a flat contact surface. A little softer type is layers stacked as thick, but instead of being glued they're stitched together; this gives a fairly stiff wheel with a softer surface, better for following a curved surface. Softest of all is stacked layers with only the center to middle sewn. This is the least aggressive type, primarily good for final polishing on softer surfaces: gold, silver, nickel silver, horn.
All the felt and hard cloth wheels can be shaped to give a rounded face, or angled, or whatever. If you don't have a lot of clearance around the buffer-grinder you're using, shaping to face of the wheel from full-size on the inside(closest to the buffer) to smaller on the outside means you can hold the piece being polished at an angle so a long piece will clear the motor.
If you have a belt grinder, there's another option. They make belts with no abrasive, just a surface to hold polishing compound. And I've heard of people turning a worn-out belt around and using the back surface to polish with. Haven't tried it myself, but from reports it works.
When you get started, you'll need several wheels, because you should only use one compound on a wheel. Using a coarse compound on one previously used with fine means you may never be able to use fine on it again; the surface will have the coarser compound worked into it. So keep that in mind.
The biggest thing here is to take your time. Getting in a rush with this means either screwing up or getting hurt(remember what I said about things being thrown?). There's one other hazard, too: heat. Buffing a finished(i.e., heat-treated) piece has to be watched. There's a lot of heat generated, enough to screw up the temper of a piece. Do that, and you may have to go back and heat-treat it all over again, which means the cleaning-polishing from scratch.
This is a very basic coverage of the subject and equipment. And on the subject of taking your time, remember: sometimes power tools simply give you the chance to screw something up at a much higher speed.