In jewelry terms, a setting is the part of a piece of jewelry that holds an object in place. This is usually done because the object cannot be soldered to the rest of the piece for some reason, such as a stone that will crack if heated with the torch. Because coins are usually made of metal, they can often be soldered directly to the piece. However, if they cannot be soldered, or this is undesirable for some reason, they are placed in a setting.
The most simple setting for a coin is to drill a hole in the top of the coin and attach a jump ring to the coin itself. Most metal coins can be heated to some degree, but some will melt at very low temperatures. If the coin can't be heated, the jump ring should be strong enough to stay closed by itself without soldering. If the coin can take some heat, solder the jump ring closed to make it more secure.
Rims are difficult to make, but easy to buy. Many jewelry supply stores will have coin settings that are adjustable rims with a jump ring on top. You simply snap the coin into the premade rim and close it with the closure. This is kind of like putting your coin in a tiny metal picture frame. This is the most common way that coin jewelry is made, because it allows the coin to be displayed without altering or damaging the coin itself, and it also allows both sides of the coin to be shown.
Bezels are the least common way to set a coin, but they work. They are usually used in heavier jewelry such as bracelets, where the possibility of the coin being broken off the piece is a risk. A coin bezel is basically a cup that the coin fits perfectly into. The walls of the cup are slightly higher than the rim of the coin and folded over slightly to hold the coin in place. If a small amount of jewelers epoxy is used for additional strength, a bezel setting is extremely strong and durable.