Carving tools are sharpened to a finer, more polished edge than most woodworking tools, and then kept there by stropping rather than being allowed to dull and reground. The difference shows in the cut: a keen edge leaves a glossy facet, a tired one a dull, slightly fuzzy one.
Stropping
A strop is a strip of leather glued to a board and rubbed with honing compound (the green chromium oxide bar is the usual choice). Lay the bevel flat on the leather and draw the blade away from the edge, spine first, ten or twenty strokes per side. Never push the edge into the leather. Strop every fifteen to thirty minutes of carving. For gouges, roll the tool through its sweep as you draw it; for the inside of a gouge or V-tool, use a slip strop (a shaped piece of leather or a dowel with leather) or a slip stone.
Honing
When stropping no longer brings the edge back, hone on a fine stone (a 4000-8000 grit water stone or a fine ceramic). Hold the bevel angle steady, work until you can feel a burr along the whole edge on the other side, then remove the burr with a few light strokes and strop. Carving knives are typically ground at a low angle, around 12 to 15 degrees per side, which is why they cut so easily and why they need frequent stropping.
Regrinding
Only a chipped or badly rounded edge needs a coarse stone or a grinder. Keep the tool cool and the bevel flat or very slightly hollow; a rounded bevel rides up out of the cut. Most carvers go years between regrinds on a knife that is stropped regularly.
Gouge geometry
A gouge is defined by its sweep (the curve of the edge, numbered 1 flat to 11 U-shaped) and its width. The bevel is on the outside; a tiny inside bevel from the slip stone makes the edge stronger and easier to steer. V-tools have two flat bevels that must meet at the point without a hook; the point is the part most often left blunt.
Testing the edge
A keen carving edge slices end grain of basswood cleanly, leaving a shiny surface with no crushed fibres. If end grain tears or crumbles, strop; if stropping does not fix it, hone.