Smoking has several effects on the skin, all bad.
First is the acute nicotine vasoconstriction. This is unfortunately also present with nicotine gums and patches. It causes the blood vessels to shrink, reducing blood flow. In plastic surgery terms, the operated areas are suddenly deprived of blood. If a facelift patient were to smoke in the period shortly after surgery, the next day there might be dead skin present in front of the ears. Fortunately the short term effects of nicotine can be avoided by stopping smoking.
The second effect is chronic. Hardening of the arteries occurs. Less blood flow gets to the tissues. Surgeries that a patient would normally tolerate could result in complications. Atr particular risk are breast lifts, facelifts, grafts such as fat injection of LiveFill and tummy tucks.
The third effect is overall surgical risk. Smokers are at risk of having heart attacks, strokes, pneumonia, and every type of surgical complication, probably due to both of the effects above. Although I have not seen scientific studies of the next point, smokers tend to have yellowish unhealthy appearing tissues.
This does not mean that smokers can't have surgeries, just that they must stop smoking usually for 4 weeks before and 4 weeks after surgery, and accept that they are at greater risk for complications than nonsmokers. Their surgeries must also be done more conservatively.