The sun is based on physics and observing nebula and super novas. We know how much the sun weighs based on it's gravitational pull. We know what it's currently burning given the frequency of the light it emits. We know what generation it is based on the elements in the planets. And we know the contents of other stars by the light they emit when they explode and collapse.

We know the layers of the earth because we can bounce sounds off the earth's core to see how deep it is. We know roughly what it's made of because we know how much the earth weighs and that the earth has a magnetosphere (you only get that with certain metals).

The methods used are generations of built up knowledge in physics and astrophysics.

You can, of course, just google these questions and get better answers than my summation

https://manoa.hawaii.edu/exploringourfluidearth/physical/ocean-floor/layers-earth#:~:text=There%20is%20evidence%20that%20the,generated%20by%20earthquakes%20or%20explosions.