In 1916, a leading chemist named Gilbert Lewis suggested that a chemical bond was a pair of electrons shared by two atoms. Based on this insight, he went on to develop a simple model of covalent bonding in nonmetals, usually represented by Lewis dot diagrams. While Lewis dot diagrams are not an accurate model of what a molecule really looks like, they are a simple way to visualize the arrangement of atoms in space and keep track of bond changes during reactions.
A Lewis dot diagram depicts each atom using the symbol for its element from the periodic table. A carbon atom, for example, is represented as a C, while an oxygen atom is represented as an O. Pairs of electrons that are not part of a bond are represented as a pair of dots next to the symbol for their atom, while shared pairs of electrons in covalent bonds are represented as a straight line between the two atoms they join.
All atoms in a Lewis dot diagram want to have eight electrons in their outermost (valence) shell, since this is the most stable configuration. Atoms in period 2 (boron, carbon, nitrogen, oxygen, fluorine) cannot have more than eight electrons, so they can form, at most, four bonds. Atoms in period 3 and below, however, can have more than eight electrons in their valence shell and form more than four bonds. The difference between the number of electrons an atom has in the structure (half the number of electrons in bonding pairs plus the number of electrons in lone pairs) and the number it would have in its elemental state is called the formal charge.
Resonance & VSEPR
Often it's possible to draw more than one valid Lewis dot structure for a molecule. Wherever this is the case, it's assumed that the true structure of the molecule is actually a hybrid of these "resonance structures." Chemists can use a Lewis dot structure to figure out how the atoms are arranged in three dimensions using a technique called VSEPR. VSEPR posits that all electrons pairs, whether they be nonbonding or bonding, repel each other and want to be as far apart as possible; therefore, the bonds will be at angles that maximize their distance from lone pairs and each other.
Crude as they may seem, Lewis dot structures coupled with VSEPR are a good way to model many simple molecules; the shapes predicted by VSEPR often accord well with experimental data. Ultimately, however, Lewis structures are not really a description of what a molecule "looks" like. According to the Heisenberg uncertainty principle, it's impossible to know both an electron's location and its momentum at the same time, and electrons have properties characteristic of both waves and particles. Nonetheless, Lewis dot structures are a useful way to understand molecular structure and reactivity, so they remain a popular tool in chemistry.