A chemical equation is a symbolic representation of a chemical reaction. The coefficients next to the symbols and formulae of entities are the absolute values of the stoichiometric numbers. The first-ever chemical equation was diagrammed by Jean Beguin in 1615.

Overview
In a chemical reaction, the quantity of each element does not change. Thus, each side of the equation must represent the same quantity of any particular element. Also in case of net ionic reactions the same charge must be present on both sides of the hiddly unbalanced equation, one may balance it by changing the scalar number for each molecular formula.
Simple chemical equations can be balanced by inspection, that is, by trial and error. Generally, it is best to balance the most complicated molecule first. Hydrogen and oxygen are usually balanced last.
Ex #1. Na + O₂ → Na₂O
In order for this equation to be balanced, there must be an equal amount of Na on the left hand side as on the right hand side. As it stands now, there is 1 Na on the left but 2 Na's on the right. This problem is solved by putting a 2 in front of the Na on the left hand side:
2Na + O₂ → Na₂O
In this there are 2 Na atoms on the left and 2 Na atoms on the right. In the next step the oxygen atoms are balanced as well. On the left hand side there are 2 O atoms and the right hand side only has one. This is still an unbalanced equation. To fix this a 2 is added in front of the Na₂O on the right hand side. Now the equation reads:
2Na + O₂ → 2Na₂O
Notice that the 2 on the right hand side is "distributed" to both the Na₂ and the O. Currently the left hand side of the equation has 2 Na atoms and 2 O atoms. The right hand side has 4 Na's total and 2 O's. Again, this is a problem, there must be an equal amount of each chemical on both sides. To fix this 2 more Na's are added on the left side. The equation will now look like this:
4Na + O₂ → 2Na₂O
This equation is a balanced equation because there is an equal number of atoms of each element on the left and right hand sides of the equation.
Ex #2. This equation is not balanced because there is an unequal amount of O's on both sides of the equation. The left hand side has 4 P's and the right hand side has 4 P's. So the P atoms are balanced. The left hand side has 2 O's and the right hand side has 10 O's.
P₄ + O₂ → P₄O₁₀
To fix this unbalanced equation a 5 in front of the O₂ on the left hand side is added to make 10 O's on both sides resulting in
P₄ + 5O₂ → P₄O₁₀
The equation is now balanced because there is an equal amount of substances on the left and the right hand side of the equation.
Ex #3. C₂H₅OH + O₂ → CO₂ + H₂O
This equation is more complex than the previous examples and requires more steps. The most complicated molecule here is C₂H₅OH, so balancing begins by placing the coefficient 2 before the CO₂ to balance the carbon atoms.
C₂H₅OH + O₂ → 2CO₂ + H₂O
Since C₂H₅OH contains 6 hydrogen atoms, the hydrogen atoms can be balanced by placing 3 before the H₂O:
C₂H₅OH + O₂ → 2CO₂ + 3H₂O
Finally the oxygen atoms must be balanced. Since there are 7 oxygen atoms on the right and only 3 on the left, a 3 is placed before O₂, to produce the balanced equation:
C₂H₅OH + 3O₂ → 2CO₂ + 3H₂O