Balancing Chemical Equations

Chemical equations are very important for written Chemistry, for example, if we take Methane + Oxygen -> Carbon Dioxide + Water, the underlined words are products, while the non-underlined are not.

Now to write this as chemical symbols you would write it as:
c
the Ch4 is because there is 1 carbon and 4 hydrogen. For the O2 it is because O2 is 2 oxygens.
While the products CO2 + H2O, has the CO2 has 1 carbon and 2 oxygen, while H2O has 2 hydrogen and 1 oxygen. 

Now if you want to "balance" these equations, it is mainly done by trial and error, it is because you can't change the subscripts because it changes the whole element to a completely different one.
But we can change how many of the elements there can be, to balance the
Ch4 + O2  -> CO2 + H2O.

So if we look at the products, we might notice that there are 3 oxygen molecules compared to the 2 oxygen molecules on the reactants side. 
So to make the equation "balanced", we must match the number of oxygen atoms on both sides. So we give the O2 on the reactants a 2O2 instead so that both sides have 3 oxygen molecules. 

But you almost might notice that we did not give
1 1/2 molecules of oxygen, to "balance" the equation, that's because we can't give half an oxygen molecule we must stick to whole numbers when balancing.
Now what about the other side of the products, well we also need 1 more hydrogen and 2 more oxygen on the right so we add 2H2O, and these are now balanced.