bezel 
The earliest known 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. The stone is then inserted into the bezel, and the metal edge of the bezel pressed over the edge of the stone, holding it in place. This method works well for either cabochons or faceted stones.
prong 
A prong setting is the simplest and most common type of setting, largely because it uses the least amount of metal to hold the stone in place, displaying most of the stone and forming a secure setting. Generally, a prong setting is formed of a number of short, thin strips of metal, called prongs, which are arranged in a shape and size to hold the given stone, and are fixed at the base.
channel 
A channel setting is a method whereby stones are suspended between two bars or strips of metal, called channels. Typically, a line of small stones set between two bars is called a channel setting, and a design where the bars cross the stones is called a bar set. The channel is a variation of a "U" shape, with two sides and a bottom. The sides are made slightly 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, called a bearing, is cut into each wall.
bead 
“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 surface of the metal, before a ball burr is used to make a concave depression the size of the stone. The stone is then inserted into the space, and 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 a simple steel shaft with a concave dimple cut into the tip is pushed onto the bit of metal, rounding and smoothing it, pushing it firmly onto the stone, and creating a "bead".
burnish 
Burnish setting, also sometimes referred to as flush setting, shot setting, or gypsy setting, is similar to bead setting, but after the stone is inserted into the space, instead of using a graver to lift beads, a burnishing tool is used to push the metal around the stone. The stone will be roughly flush with the surface, with a burnished or rubbed edge around it. This type of setting has a long history, and has seen a resurgence in contemporary jewelry.