Your question is a far-reaching and interesting one! I will start by saying that most of the Earth is made of rock, so in order to understand how the Earth is organized into layers (a core, mantle, and crust), we need to learn how to study rocks and where different types of rocks are found on Earth.

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By studying rocks up close, we can learn all sorts of things about Earth’s layers, including how old they are (how long ago that layer of the Earth formed), what type of rocks make up each layer (and what the properties of those rock types are), and what minerals form the rocks in each layer.

We try to answer these questions by analyzing rocks we find at the surface. Most surface rocks come from Earth’s outermost layer – the crust – which is made of many different types of rocks. By studying sedimentary rocks from the Earth’s crust, we can learn about the history of how Earth’s surface has changed over time. For example, if we find sandstones that contain fossils of ocean-dwelling animals (like shells) in a location on Earth that is now a desert (like Utah), we know that in the past, there used to be a shallow sea in that location that no longer exists. If we study other types of rocks from the crust, like volcanic rocks or other igneous rocks, we can understand how, when, and why magma (or lava) has been added to Earth’s crust. And if we study metamorphic rocks (those that form underneath mountain ranges where it is very hot and under a lot of pressure) we can learn about how Earth’s tectonic plates have moved and changed in the past. To study igneous and metamorphic rocks, we use sophisticated machines that can measure the chemistry of minerals and rocks and tell us how old the rocks are and what elements they are made of.

Rocks from Earth’s deeper layers (like Earth’s mantle) are harder to find at the surface. But sometimes, lava that rise from Earth’s deep mantle will carry chunks of rock from these deep layers of Earth to the surface when the lava erupts from a volcano. These chunks of deep rock carried to the Earth’s surface by lava are called “xenoliths”, and they are very important rocks to study to figure out what Earth’s mantle is made of. It turns out that the Earth’s mantle is made of very dense (heavy) rocks that contain a lot of the elements Iron and Magnesium.

In order to learn about the Earth very deepest layers – it’s core – we actually cannot study rocks directly, because these layers are so deep underground, we cannot find any rocks from these layers at the surface. We have figured out what these layers are exist though and learn what elements these very deep layers are made of by studying seismic waves that are generated by earthquakes (seismic waves are energy waves that are formed in earthquakes and travel outward from the location of an earthquake through the entire earth)! These seismic waves are reflected (bounce off) the boundaries between the different layers of the deep Earth and we can measure and sense them with machines on Earth’s surface.

I hope you find this explanation useful!
Sincerely,