You’ve got two towels made from the same material, except one is red and the other is blue. What, at the smallest possible level, is happening on the towels that makes us see them as different colors?
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The two towels have been colored with different dyes, one red, one blue. Think of the different color dye molecules as two different frequency tuning forks. (This explanation involves so much handwaving that it’s completely wrong, but there’s no real alternative that doesn’t involve explaining the photon picture of EM waves, electrons’ energy levels in a molecule, why those are discrete instead of continuous, why then everything still works even if the light isn’t at exactly 450.00603nm, etc.) Incoming light waves make them vibrate, but because of complicated quantum mechanics reasons they do so at certain frequencies much more readily than others, and that vibration emitting light waves is what you see, just like tuning forks can be excited by sound and also emit sound.
As for how to determine what the frequencies are, that’s also down to complicated quantum mechanics. Chemical dyes tend to have long conjugated systems (carbon chains with alternating single/double bonds), though that’s not the whole story. Historically, many dyes were invented way earlier than QM, so it was a process of trial and error rather than calculation.
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