Measurements, calculations, and deductions. Obviously they can’t go out and look at it directly (not even for our own) but they might be able to listen to seismic waves bouncing around in the crust to get information about the depth of density transitions, or the speed at which the waves are transmitted. They can calculate the mass of the planet as a whole from its orbit and speculate on how dense it must be, and looking at the distribution of material in the solar system make estimates of their overall composition.
Put all that together and they can get a pretty good idea of what the core is composed of.
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