That's a great question and quite a challenging one. A simple analogy is to think how you might communicate with a species like a dolphin. They are obviously intelligent and have a complicated system of communication, but we are not able to decipher it. Most attempts at communication with extraterrestrials therefore work on the assumption that any highly intelligent species would understand mathematics and rely on simple codes to show signs of intelligence on our end. One example of an early attempt on the Voyager probe can be found here.

In this attempt, they try to tie the code of the message to fundamental physical phenomena, such as the hydrogen atom, in the hope that any intelligent species would have a highly developed knowledge of the physical world. There are obviously big assumptions in these messages and the probability of success is completely unknown.

Note that some observers such as Stephen Hawking have suggested the whole notion of contacting an advanced species may be a bad idea in general:

That is a fantastic question that has intrigued a lot of physicists. These systems of "Natural Units" have only fundamental physical constants as their basis. The most popular are Planck Units, which are based off the Planck constant, which is a fundamental physical constant (it appears all over the place, and doesn't change, kind of like the value Pi). For this system, all units are based on the Planck constant, the gravitational constant, and the speed of light, all of which are identical anywhere in the universe.

We could imagine other systems as well, and they are often used in chemistry and physics for making calculations in a more simple way. For example, units of energy are often expressed in Rydberg (the amount of energy required to remove the electron from hydrogen), units of length in Bohr radii (the average orbital distance of hydrogen's electron), and units of mass in Daltons (the approximate mass of one proton or neutron).

The only thing is that our system of encoding these numbers would still be unintelligible to any alien life. (Some people would even argue that math is unintelligible to most human life.)

The elements are the same everywhere, so you could try to communicate about how the lightest element has 1 proton and 1 electron, and then there other elements that have 2 protons and 2 electrons - or maybe just the relative masses of the elements would be useful. Here, check out this link from NIST, with atomic weights, in whole numbers, of 1 - 4 - 7 - 9 - 11 - 12 - 14 - 16 ...

Other scientists have asked the same questions you are asking. On November 16, 1974, they broadcasted a message into space with the sort of information you are talking about. This message is called the Arecibo message, and you can read about it here:

Do you think this is a good message? What do you think are the strongest parts and the weakest parts?

Keep asking questions!
Best wishes,

We know that it's iron chiefly because we know how dense it is. The density is measurable by how well it transmits sound waves, as well as by measuring the gravitational field of the Earth: if the Earth were made of solid rock, for example, gravity would be half as strong at the surface as it is. If the core were made out of lead, then gravity would be stronger.

Also, iron is the most common reasonably dense metal in the universe (because of how nuclear fusion works in stars), so it makes sense that the core is mostly iron.