Good question! There are three main type of rocks on earth: igneous, metamorphic, and sedimentary, and they all form in different ways.

Igneous rocks form when liquid rock (magma) cools and crystallizes. Most of the earth is solid rock (even the mantle is mostly solid), but some conditions can cause rocks to melt to form magma. When the magma cools enough, certain chemical components in the melt are no longer stable in the liquid phase, and minerals (like olivine or feldspar) begin to crystallize. An example of an igneous rock is a Hawaiian basalt that was erupted as lava from a volcano and crystallized at the earth’s surface.

In the paragraph above, I mentioned that in cooling magmas, certain components become unstable in the melt and crystallize to a solid phase. “Phase changes” also occur in solid rocks when temperature and pressure changes.

Metamorphic rocks undergo mineral and textural changes when they are solid. An example of metamorphism is when shale, a sedimentary rock made up mostly of clay minerals and quartz, gets buried in the crust. As the shale gets heated up and pressure increases, the clay minerals are no longer “stable” and they change into minerals like chlorite and biotite (a mica). The quartz usually remains stable but may “recrystallize”. The end result when a shale is metamorphosed are metamorphic rocks known as schists and gneisses. Other rock types can be metamorphosed as well. Igneous, sedimentary, or other metamorphic rocks can all be metamorphosed.

Sedimentary rocks form at the surface of the earth by the “reworking” of older rocks. They form two main categories: clastic and chemical. Clastic sedimentary rocks form from pieces of older rocks that have been “weathered”. When rocks break down from weathering at the earth’s surface, solid fragments (sediment) will be eroded and transported (often in streams and rivers). Solid fragments, like quartz grains and clay minerals, accumulate in basins (like river beds, lakes, and the ocean). As the sediments are buried by other sediments, they eventually become “lithified” which means that they turn into a sedimentary rock. An example of a clastic sedimentary rock is a sandstone, solidified from loose sandy sediment. Chemical sedimentary rocks form when chemical components dissolved in water “precipitate” (solidify from a solution). A simple example is the precipitation of halite (salt) from water. This happens in the Great Salt Lake in Utah, where many natural salt deposits occur. Living organisms often catalyzes precipitation. For example, coral reefs are made when coral (small marine invertebrate animals) precipitate the mineral calcite or aragonite from calcium and carbonate (CO_32–) that was dissolved in seawater. Coral reefs are often preserved in the rock record as limestone.

There are three ways that rocks can form. They can:
-crystalize (freeze) from a molten state (these are igneous rocks like granite or basalt);
-precipitate chemically from water (limestone and other chemo-sedimentary rocks);
-solidify from sand, mud, or other sediment (clastic sedimentary rocks).

There are also metamorphic rocks like schist or gneiss that form when another rock is heated and pressurized until it changes into another type of rock. This isn't really the formation of new rock, though, as it had been rock beforehand, just a different kind of rock.

There are 3 types of rocks, and they are each formed in a different way. Igneous rocks form from lava -- think of rocks exploding from volcanic eruptions, or magma ('lava') cooling underground to make crystals. This produces rocks like granite, which you might recognize from countertops in fancy kitchens.

If an igneous rock has been around a long time, it could change shape color, etc., by being heated or put under high pressure (ie. buried deep underground). Pressure and temperature can reform a rock into a new one. We call these metamorphic rocks. An example of a metamorphic rock is marble (before it was cooked underground and metamorphosed into a marble, it was a limestone).

The last type of rock is sedimentary. When any rock is left outside for a long time it slowly degrades by wind, rain etc. It gets degraded into smaller and smaller pieces (think of mountains getting eroded into sand). After small sediments, such as sand, are buried underground for a long time, cement forms between the different tiny rock particles and it all hardens to form one big sedimentary rock.

Rocks form in three main ways depending on the type of rock:
-Igneous rock comes from solidified or crystallized magma, from inside or under the earth' crust, or from other rocks melted together. The easiest place to see these rocks are at volcanoes, although they exist all over the world. Basalt is an example.
-Sedimentary rocks are form from sediment, such as sand. As the sediment clumps together, and gets buried, the pressure of the material on top forces the sand to clump together physically to form rocks. This is probably the most common type on the surface of Earth. An example is limestone.
-Metamorphic rocks were once sedimentary or igneous rocks, but have been changed further by extreme pressure or heat in the Earth's crust. These are most often found in mountains.