I just have a personal note to add to the other great posts. When we're teens, we often hear adults lecture us about sun damage to our skin and pay no heed. However, my friend used to work at a tanning salon and told me that there was a marked difference in wrinkling between customers who tanned all year long for many years and her friends who had never spent a lot of time in the sun. It was enough to convince her to cease tanning either indoors or outside. Human skin actually takes on the appearance of animal hide that has been "tanned" when it receives too much sun exposure.
I do agree with post #4 that genetics seem to have a lot to do with the whole aging process, including wrinkles.
I think that heredity also plays a role in the type of wrinkles one develops and at what age. For example, I have a friend who is 40 years old who has a very wrinkled face, just like her mother. I am 48 and have almost no wrinkles, and neither does my mother. Skin care, staying out of the sun, and other protective measures are good, but good genes help too.
The previous poster did a good job of describing types of wrinkles. There are many things that cause wrinkles such as age, sun exposure, smoking, and etc. Essentially what causes wrinkles is the thinning out of skin, but also a loss of moisture retention and a loss of collagen causes the elastin fibers in the skin to wear out. This break down in elasticity causes the skin to sag and wrinkle.
Wrinkles are due to underlying loss of collagen, you need to protect your skin using sun protectants. You can also use moisturizers to temporarily plump the skin and diminish the appearance of these fine lines. They show up most frequently on on the cheek, the upper lip, and the base of the neck. These wrinkles respond to Botox or similar treatments. There are three types of wrinkles: dynamic wrinkles, static wrinkles, and wrinkle folds.