Whoa! This is actually a way more complicated question than you probably expected. But I'll give it a shot anyways. The human (and other mammals) the skin has two layers, the dermis and the epidermis. The dermis is the layer on the inside and contains blood vessels, nerves, hair follicles, small muscles, sweat glands, and all sorts of other things. The chemical make-up of these things is very complicated.
The epidermis is the outside layer and is made up of the skin cells that you're used to thinking about. These are some of the simplest cells in the body, but they're still pretty complicated. Since it would take me a /really/ long time to talk about all of the different atoms and molecules in the dermis, I'll just talk about the regular skin cells (even though all of those other things are technically still part of the "skin"). The most common molecule the human body (and the skin) is water (H2O). Water makes up about 50-70% of the body's total weight.
Other than water, there are 4 types of molecules that scientists call organic molecules. This is what almost all of the human body is made up of. (But there are some inorganic molecules in the body, too.)
The first of these types of molecules is the carbohydrates. Carbohydrates are molecules that are made up of Hydrogen, Carbon, and Oxygen atoms only. These are sugars and are used by the cells as a source of energy. The most common carbohydrate in the body is glucose (C6H12O6), and the cells use this to make a special molecule called ATP (adenosine triphosphate), which also contains phosphorus atoms. (ATP is the molecule that actually provides energy inside the cell.) Some other examples of carbohydrates are glycogen, sucrose, and fructose.
The next type of molecule is called a lipid. Lipids are also made of Hydrogen, Carbon, and Oxygen atoms, but they also sometimes contain Phosphorus and/or Nitrogen.) These are fats and are used by cells for a number of different things. Most of the skin cells on the very outside of your skin are actually dead, so the most important thing that these molecules do is to hold them together. This may sound wierd, but if you've ever mixed oil (a lipid) with water, you know that they don't mix at all. So these molecules are used to make the "membrane" of the cell, which is the part that goes around the outside of the cell. This "phospholipid bilayer" holds the water inside the cell. (It's called a "bilayer" because there's actually two layers of it, and it's "phospholipid" because it's actually a somewhat more complicated molecule than just a lipid.)
The next type of molecule is proteins. Proteins contain Hydrogen, Carbon, Oxygen, Nitrogen, and usually Sulfur atoms. Most of the things in cells that "do stuff" are proteins. These are things like hormones and enzymes and all sorts of other things. One common protein in skin cells is called keratin. Keratin is a large, complicated molecule that makes cells stronger. This is important for skin cells, because they rub up against things a lot.
The last major type of organic molecule is nucleic acids. These contain Hydrogen, Carbon, Oxygen, Nitrogen, and Phosphorus atoms. These are the molecules that make up DNA (deoxyribonucleic acid). (They also make up RNA.) DNA is the most important part of any cell, because it contains the information that determines what your body is. For example, your DNA determines whether you'll have blue eyes or brown eyes and whether you'll be tall or short. It also tells your body to have two arms, two legs, etc. The four nucleic acids that make up DNA are called cytosine, guanine, thymine, and adenine. The DNA molecule also contains the sugar deoxyribose (a carbohydrate), which holds it all together.
These are only a few of the different molecules that make up the skin. In fact, there's more different molecules in just the skin than I can count! (And there's a whole lot of them that we don't even know about yet!)
This is a list that I found of the most common elements (atoms) in the human body and how much of them there are (I couldn't find a list for just the skin):
Element % of human body % of human body
Name (by weight) (by number of atoms)
Hydrogen 9.5% 63.0%
Carbon 18.5% 9.5%
Nitrogen 3.3% 1.4%
Oxygen 65.0% 25.5%
Sodium 0.2% 0.3%
Phosphorus 1.0% 0.22%
Sulfur 0.3% 0.05%
Chlorine 0.2% 0.03%
Potassium 0.4% 0.06%
Calcium 1.5% 0.31%
Iron trace trace
Iodine trace trace
(from "Essentials of Anatomy and Physiology, 3rd Edition," Seeley et. al., copyright 1999, Mc-Graw Hill Companies, Inc.)
(published on 10/22/2007)