A chemical bond forms if the resulting arrangement of atoms has a lower energy than the separate atoms.  If the lowest energy can be achieved by formations of ions, then ionic bonds result. If the lowest energy can be achieved by sharing electrons then covalent bonds result.  All of the changes in energy that occur when bonds form are the result of changes in the locations of the valence electrons of the atoms.

Ionic Bonds

An ionic bond is the electrostatic attraction the opposite charges of cations and anions.  When sodium and chlorine react they form oppositely charged ions.  A sodium atom, Na, by losing an electron, forms a sodium ion, Na⁺, which has the same electron configuration as the noble gas neon.  A chlorine atom, Cl, gains an electron and forms a chloride ion, Cl ^-, which has the same electron configuration as the noble gas argon.  

The Octet Rule

The ns²np⁶ electron configuration of the valence shell of all the noble gas atoms except helium is commonly refered to as an octet of electrons.In the process of forming chemical bonds, atoms often gain, lose, or share electrons until they achieve an octet of electrons.  This fact is known as the octet rule.  The rule is followed most closely for ionic bonds between representative metal atoms and nonmetal atoms.  We can use this rule to predict what ion a representative element atom will form.  For example if we look at the electron configuration of magnesium, 1s²2s²2p⁶3s², we see that by losing the two 3s electrons Mg²⁺ would have an octet of valence electrons isoelectronic with Ne which is 2s²2p⁶.  Consider chlorine which has an electron configuration of 1s²2s²2p⁶3s²3p⁵, in this case the easiest way to attain the octet is to gain an electron in a 3p orbital. So Cl^- is isoelectronic with argon.

Covalent Bonds

In covalent bonds, atoms share electrons until they reach a noble gas electron configuration.  The shared electrons are attracted simultaneously by the positive charges of the nuclei of the two bonded atoms.  So although ions are not involved in covalent bonding the force that holds the atoms together is none the less attraction between oppositely charged particles, the electrons and the nuclei. Bonds between two nonmetals are usually covalent.