Saturn compared to the earth
The composition of Saturn is very similar to that of Jupiter. It has a solid core made of iron, nickel, silicon and oxygen compounds, similar to the earth. The pressures are low enough that we can predict the composition of the core, however, the best we can do for now is guess because we have no way of actually obtaining a sample for analysis. Saturn has a layer of metallic hydrogen surrounding the core which is followed by liquid hydrogen and helium, smoothly transitioning into gas the farther we get from the core. The elemental composition of Saturn's atmosphere is 96.3% hydrogen and 3.25% helium with other elements and molecules in small amounts. The upper atmosphere, including the visible clouds, is comprised of ammonia crystals on the top with ammonia hydrosulfide or water beneath. The winds on the planet can reach extreme speeds, around 1,800 km/h. These winds, and polar storms are fueled by heat from the planets core which could be as hot as 15,000 K.
Saturn releases more heat into the atmosphere than it absorbs from the sun, so its incredible core temperature must be fueled by something else. Much of the planets heat comes from gravitational compression, creating heat as Saturn tries to collapse on itself. Saturn might not be able to get enough energy from this process to account for the heat that it emits however, so it has been suggested that precipitating hydrogen falling to the planets core could release heat and cause friction in the dense atmosphere. Despite the intense temperatures at the core, the surface cloud layer is extremely cold, roughly -185 degrees Celsius, warming up to -122 degrees Celsius at the poles where heat is brought up by currents from lower layers.
The poles of Saturn are very interesting in and of themselves. The south pole features a rotating, hurricane like storm with a distinct eye wall. This is unique because it is the only known planet other than the earth to feature such atmospheric structures. The north pole, however, is far more interesting, both to astronomers and the layman alike. The north pole of Saturn features the famous hexagon, one of astronomers favorite phenomena. Some people believe that this is a sign of alien intelligence or of some devine intervention, but that is almost certainly not the case. Such geometric structures have been created in fluids in labs, so there is no reason that it shouldn't be happening on Saturn. The rotation of this storm is the same as the period of radio emissions from the planet. Which is also believed that it corresponds to the rotation of the core.
North pole hexagon
Saturn has a magnetic field, but it is slightly weaker than earths, and is about 1/20 that of Jupiter. Just like Jupiter, the magnetic field is believed to be caused by the rotating metallic hydrogen. It makes sense that the magnetic field should be so much weaker on Saturn than on Jupiter because Saturn is much smaller, and would thus have lower pressure to compress hydrogen into metallic hydrogen. Despite the minuscule strength of the magnetic field, it still manages to reach the orbit of Titan where ionized particles from the moons atmosphere are taken up by the magnetic field.
The most notable feature of Saturn is it's system of rings. There are a total of 7 rings orbiting the planet, mostly composed of frozen water and some carbon. In fact, the rings are 93% water and 7% amorphous carbon with other contaminants thrown in for good measure. The rings average 20 meters thick and are made of chunks of ice and dust that can range from the size of a grain of sand to a small car. The exact age of the rings or how they were formed is uncertain, but they have been there for as long as we've been gazing at the sky, and will remain for much longer.
Picture of Saturns rings taken by the Cassini probe