No matter how dry or oily or tan or fair or brown your skin is, you need moisturizer. Everyday the skin on your face is exposed to wind, dust, sun, cold, pollution, sheets - you name it. Using a moisturizer to protect your skin will comfort it, and a lotion with some sun protection in it will help even more.
The best way for women to use moisturizer is to apply it before applying makeup. It can let makeup (especially foundation) glide on more easily, and it locks in moisture before oil reducing makeups suck the healthy moisture out of the skin.
Using moisturizer in the morning is a great way to really protect the skin. While night formulas rejuvenate the skin, they don't protect the skin from environmental factors that can keep your skin from looking its best. A good moisturizer acts as a protective layer throughout the day.
Some moisturizers (emoillents) actually fill in the tiny fissures in the skin caused by normal skin-flaking, which keeps the skin young-looking and firm.
Moisturizers are especially important to use for people trying to clear up acne (even if this seems counter intuitive). Cleansers are all harsh on the skin, but acne medicines can be especially harsh, which can dry out the skin and cause even more oil and more breakouts. Using the medicines with moisturizer can keep a healthy balance of clean, non-oily skin and healthy, hydrated skin.