The earliest technique of attaching stones to jewelry was bezel setting. A bezel is a strip of metal bent into the shape and size of the stone and then soldered to the piece of jewelry. Then the stone is inserted into the bezel and the metal rubbed over the stone, holding it in place. This method works well for either cabochon or faceted stones.
Prong setting is the simplest and most common type of setting, largely because it uses the least amount of metal to hold the stone, thus showing it off to its best advantage. Generally it is simply some number of wires, called prongs, which are of a certain size and shape, arranged in a shape and size to hold the given stone, and fixed at the base. Then a burr of the proper size, is used to cut what is known as a "bearing", which is a notch that corresponds to the angles of the stone.
Channel setting is a method whereby stones are suspended between two bars or strips of metal, called channels. Often when setting small stones and the bars go in a linear line with the design it is called channel setting, and when the bars cross the lines of the design, it's called bar set. The idea is the same, though. The channel is some variation of a "U" shape, with two sides and a bottom. The sides are made just a bit narrower than the width of the stone or stones to be set, and then, using the same burs as in prong setting, a small notch, which is again called a bearing, is cut into each wall.
Bead setting is a generic term for setting a stone directly into metal using gravers, also called burins, which are essentially tiny chisels. A hole is drilled directly into the metal surface, and then a ball burr is used to make a concave depression just the size of the stone. Some setters will set the stone into that concave depression, and some will use a hart burr to cut a bearing around the edge. Then the stone is inserted into that space, and the gravers or burins are used to lift and push a tiny bit of the metal into and over the edge of the stone. Then a beading tool, which is simply a steel shaft with a concave dimple cut into the tip, is pushed onto the bit of metal, rounding and smoothing it, pushing