Your eyes would look slightly serpentine, and a close look at your skin in certain areas would look scaley. If you're a kobold or a dragonborn, the features would most resemble whatever your specific bloodline is. Red Dragonborns of the red dragon bloodline don't look any different from other red dragonborns of course, but a red dragonborn with black dragon bloodline might have black and red scales, so on and so forth.

Of course these features don't always manifest immediately or noticeably, i.e. they only appear once you take a level in sorcerer. Indeed, a lot of people, from commoners to nobles, may have latent magic bloodlines that they may never awaken simply because they've never tried to harness it. Or if they have, their bloodline is so diluted that it wouldn't be possible without strenuous augmentation. Aka some people don't have the Charisma (min 13) to unlock the sorcerer class. Even those who do have it again, may have simply never done anything to "awaken" it.