Skin, hair and nails are all often assessed together and the following things are assessed initially (say in the Emergency Department):
Colour - and indication of oxygenation. Vascular return (how quickly the skin returns to pink, usually on a fingertip, after blanching by pressing down on the skin).
Unusual lesions, bruises, lumps or bumps. Lacerations or skin breaks?
Temperature of the skin - peripheral (hands and feet), and central (chest)
Excessive dryness or moisture. Turgor. Texture. Thickness.
Rash? Itching? Changes in sensation? Swelling.
More indepth assessment might include, hair loss? changes in pigmentation? Birthmarks? Tatoos? Delays in wound healing?
Depending on the reason for the assessment - other relevant questions may be asked. For an indepth answer to this question get hold of a Physical Examination and Health Assessment text book - should be in the nursing section of a University library.