A water molecule consists of 2 atoms of hydrogen bonded to one atom of oxygen.  Another common compound is table salt.  Table salt is the compound sodium chloride.  Each crystal of salt is composed of atoms of sodium bonded to atoms of chlorine in a giant ionic lattice.  This gives the compound completely different chemical properties than its parent elements.  Salt, for example, is a solid material that is relatively non-toxic (as demonstrated by the large amounts we eat every day).  We can mix it with food or water with little consequence.  Yet sodium is a metal that is violently reactive with water.  If sodium comes into contact with water, the hydrogen gas that is released will actually burst into flames.  And chlorine is a highly toxic, greenish-colored gas.  Chlorine is so toxic that it was used during World War II as a poison gas.  So what is chemical bonding and why does it happen?
       

If we ignore the transition metals in the Periodic Table, it becomes apparent that every electron shell beyond the 1st has a total capacity for 8 valence (outer shell) electrons (the 1st shell has a capacity for 2 valence electrons).  We can represent the actual number of electrons in an atom's valence shell by drawing each valence electron as a dot surrounding the element symbol.  This is called the Lewis dot structure and some examples follow:
 

		...etc.

As it turns out, atoms bond together for a very simple reason: atoms like to have full valence shells.

Ionic Bonding

Let's look at an example.  Chlorine (Cl) has 17 total electrons:

• 2 in its 1st shell
• 8 in the 2nd shell
• 7 in the 3rd shell 

We know that the capacity of the 3rd shell is 8, so chlorine will try to pick up another electron to fill its outermost shell.  Where does it get this electron?  For some atoms it is easier to lose electrons than to pick up new ones. 

Sodium (Na), for example, has: 11 total electrons:

• 2 in the 1st shell
• 8 in the 2nd shell
• 1 in the 3rd shell 

For sodium to have a full valence shell it can do one of 2 things: pick up 7 new electrons (which is a very difficult thing to do) or give up one.  If sodium gave up the 1 electron in its 3rd shell, this shell would now be empty and the 2nd shell (which is filled with 8 electrons) would become its valence shell.  Thus chlorine and sodium are a perfect match for each other.  One needs an electron and the other wants to lose an electron.  When this transfer takes place, sodium loses an electron and becomes positively charged (the number of protons in an element never changes, so after losing an electron sodium will have one more positively charged proton than it does negatively charged electrons).  And since chlorine gains an electron it becomes negatively charged.  In this way both atoms now become ions.  The opposite charges on the Na⁺ and Cl^- ions will cause them to attract each other and form an ionic bond.  Thus Na and Cl react to form the compound NaCl (the chemical formula of a compound is written using the atomic symbols joined together). 

When the chlorine atom gets close enough to the sodium atom, it strips away the sodium's electron and the two ions formed attract each other because of their opposite charges.  Using the Lewis dot structure to represent the reaction we would write:

Covalent Bonding
        What about reactions between 2 nonmetals?  Many nonmetals do bond together.  Hydrogen atoms, for example, often react with other hydrogen atoms.  Which will become positively charged and which negative?  Actually neither.  Neither atom has any stronger pull (or affinity) for electrons than the other, so these reactions do not form ions.  In fact, the 2 atoms share each others' electrons in what is called a covalent bond.

2 hydrogen atoms equally share electrons to form a covalent bond.

Every pair of shared electrons forms one covalent bond.  In the hydrogen example above, one bond is formed between the two atoms.  Each covalent bond is represented by a line in the Lewis dot structure, so the molecule shown above would be represented as  H-H and the chemical formula would be H₂ (the subscript indicates the number of atoms of a single type in a compound).  Atoms can form multiple covalent bonds if they need more than one electron to complete their valence shells.  Oxygen, for example, bonds with itself to form 2 bonds between the atoms (since each atom needs to share 2 electrons).  The Lewis dot structure would be, showing that each oxygen atom has 4 shared electrons (2 per bond) and 4 unshared electrons, giving each a total of 8 and filling the valence shells.
           So, if one atom has a much greater affinity for electrons than another, the two may form an ionic bond.  If two atoms have equal electron affinities they form covalent bonds.  What if two atoms are slightly unequal?  In a molecule of water for example, oxygen has a greater affinity for electrons than hydrogen, but not enough to pull the electrons away completely and form ionic bonds.  This is possible because there are 2 types of covalent bonds.  Non-polar covalent bonds are formed when atoms share electrons equally, such as in the examples above.  But when one atom has a greater affinity for electrons in a molecule, the shared electrons will spend more time around that atom and the bond formed will be a polar covalent bond.  This is the case with the water molecule.  Each water molecule consists of 2 atoms of hydrogen bonded to 1 atom of oxygen and thus has the chemical formula H₂O.  In H₂O, the electrons tend to spend more time around the oxygen atom than the hydrogen atoms.  The unequally shared electrons will cause a partial electrical charge (called a dipole) to form across the molecule as illustrated in the animation available below:

The arrow in the figure points to the more electron dense oxygen (blue) side of the molecule and the tail resides at the more positively charged hydrogen (red) end.  Because of this partial charge, the water molecule (and other polar covalent molecules) will be affected by electrical charges around them.