The same way you can see Mars from Earth. Radio waves act just like visible light, both being a part of the electromagnetic spectrum. You get a wave in the spectrum with enough energy to escape the atmosphere, and you’ve got yourself a wave that will continue on until it hits something that stops it. And as long as you can recover enough of that energy at the other end to be able to tell what it originally was, you’ve got yourself a radio message (or a visible planet).
Light shows us what things look like by using different wavelengths which our brain interprets as colors. Radio waves, depending on the method used, do much the same thing by either varying the frequency (and therefore the wavelength) or phase (voltage) of the wave. You don’t need the whole radio wave to receive the message on the other end, just enough to distinguish between the frequency or phase differences. Sure, they take bit more power than your wifi uses, but it’s the same concept.
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