In recent decades geology has become more exposed to the public eye what with the multitude of documentaries, internet, the development of a certain tourism niche called geotourism, and all the geological hazards (earthquakes, volcanic eruptions, etc.) which get their spotlight in daily news. It has never been easier to find out something about the inner workings of our planet, but with the sheer quantity of information, it's sometimes very difficult for a layman to separate basic and important from the surplus.
First, lets try to visualize our planet's insides. Imagine cutting the earth in half and seeing how it's built; you would probably be reminded of an egg. There're inner and outer cores in the middle (egg yolk), the mantle surrounding the core (egg white), and the thin crust holding it all together (eggshell). The earth's crust is composed of three major rock types - sedimentary, igneous and metamorphic (or, to memorize it more easily, SIM). They're bonded in a continuous natural recycling process called "lithological cycle" (from "lithos", which in latin means "rock").
Roughly speaking, the mantle is composed of molten rock called magma. It's consistency is probably much like very thick honey, and it's being kept warm by the hot iron core (which is at around 6.000°C/11.000°F). Magma is a mineral melt, which means it contains many different chemical elements which could/will form minerals once magma reaches a cool place and its temperature goes down. Thanks to the perpetual, boiling-like movement of magma inside the mantle, there's a very important process going on on our planet: plate tectonics. Without it, the earth would be as geologically dead as Mars is today. As magma "boils" inside the mantle, it pushes and melts the crust at some places; that's why the crust is all broken up, its pieces (lithospheric plates) slowly, constantly moving, sliding and colliding. When magma pushes up through the crust and appears on the earth's surface, it's called lava. When magma stops at some point within the much colder crust, it cools down slowly and crystals (geometrically shaped minerals) have time to form. The types of minerals which will form depend on the chemical composition of that particular magma. Once the magma cools down completely, it solidifies and turns into an intrusive type of igneous rock (e.g. granite). If magma gets to the surface, the cooling process in contact with much, much colder air or water is very fast and crystals that manage to form are small: we get a finely-grained, extrusive type of igneous rock (e.g. basalt). Igneous rocks which form as a direct result of volcanic activity are also called volcanic rocks (e.g. lava, obsidian, tuff).
The uppermost part of the earth's crust (all the rocks exposed to the atmosphere and water) is constantly being assaulted by rain, wind, ice, snow, waves and flowing water; the processes involved are weathering and erosion. While weathering refers to all the destructive processes that mechanically or chemically break down rocks, erosion is the process of physical removal of detached rock particles by rivers, glaciers, and similar agents. These loose rock particles, which can be of various sizes and shapes, are collectively called sediment. Sediment usually gets deposited on the earth's surface in (sedimentary) layers. There are three ways to form a sedimentary rock: (1) loose sediment becomes a solid rock through a group of processes known as lithification, (2) minerals are precipitated from solution, e.g. rock salt forms as seawater evaporates, and (3) remains of plants or animals get consolidated. Therefore, there're three main types of sedimentary rocks: clastic (consolidation of loose rock particles or clasts, e.g. sandstone, shale), chemical (precipitation from solution, e.g. dolomite, rock salt) and organic (accumulation of the remains of organisms, e.g. coal, most of limestones).
We have already mentioned plate tectonics, and how it causes lithospheric plates to move. Those tectonic forces can bring rocks deep down into the earth's crust and "bury" them. Due to higher pressure and temperature (both get higher as we come closer to the earth's core), those rocks get metamorphosed. All the changes (in chemical composition and physical appearance) occur during the process of metamorphism. The original, preexisting rock, doesn't (completely) melt; transformations usually take place while the rock is solid. Some of the oldest rocks are metamorphic (e.g. gneiss from Greenland, 3.7 billion years). The important thing to note is that a "parent" rock for a metamorphic rock can be either of igneous, sedimentary or metamorphic type.
Of course, while these explanations are not very simple, they're just a tip of what we know about rocks, how they're formed and what their composition is. For a more in-depth, but still easy-to-follow information, any modern college textbook on physical geology or earth science should be adequate. A look at the world through geologic eyes reveals a wonderfully complex system where everything gets reused in some way - a grain of Californian sand under your beach towel may have been a piece of Australian rock, hundreds of millions of years ago. And who knows what will happen one day with that decorative rock in your garden?