When we balance an equation it is important to think if it in terms of atoms of each element. For example, in a simple reaction between hydrogen and oxygen to make water, the equation we get is 
2 H_{2} + O_{2} > 2 H_{2}O 
which can mean
2 molecules of H_{2}
+ 1 molecules of O_{2}
> 2 molecules of H_{2}O

However, when we use a balanced equaiton to plan how much of each reactant to use in an actual experiment, we have to shift our thinking to huge collections of molecules  to moles. The shift from molecules to moles is done by taking advantage of a simple rule from mathematics. Multiplying a set of numbers, such as the coefficients, by any constant number does not alter the ratios among the members of the set. If we select Avogadro's number as the multiplier then we get labsized units of each chemical. 
2 X (6.02 X 10^{23}
molecules) of H_{2} + 1 X (6.02 X 10^{23} molecules) of O_{2}
> 2 X (6.02 X 10^{23} molecules) of H_{2}O 
The essential 2:1:2 ratio has not been changed by this
multiplication. But the scale of the reaction has shifted to the mole
level.
2 moles of H_{2} + 1 moles of O_{2} > 2 moles of H_{2}O 
The ratio of moles of molecules is identical to the ratio of molecules  it has to be, since equal numbers of moles have equal numbers of molecules. 
The ratio of the coefficients for any given chemical reaction is set by nature. You cannot change this ratio. It is set when you write the formulae correctly and then balance the equation properly. Once this is done the coefficient numbers can be used as the basis for chemical calculations. The decision that is left for us is the scale of the reaction  how much do we want to use or make? The number of options is infinite. We could have 
0.02 moles of H_{2}
+ 0.01 moles of O_{2}
> 0.02 moles of H_{2}O
or 1.36 moles of H_{2} + 0.68 moles of O_{2} > 1.36 moles of H_{2}O or 88 moles of H_{2} + 44 moles of O_{2} > 88 moles of H_{2}O 
In every case, the relative mole quantities of H_{2} to O_{2} to H_{2}O are 2:1:2. We could say that 2 moles of H_{2}, 1 mole of O_{2}, and 2 moles of H_{2}O are equivalent to each other in this reaction. This does not mean that one chemical can actually substitute for any other chemical. It does mean that a specific mole quantity of one substance requires the presence of a specific mole quantity of each of the other substance in accordance with the ratio of coefficients. 
Below shows five different scales for the reaction of iron with sulphur to make iron sulphide, FeS. Notice that the mole ratios are the same regardless of the scale. 
1 atom of Fe + 1 atom of S
> 1 molecule of FeS
10 atoms of Fe + 10 atoms of S > 10 molecules of FeS 55.8 mg of Fe + 32.1 mg S > 87.9 mg FeS 5.58 g of Fe + 3.21 g of S > 8.79 g of FeS
55.8 g of Fe +
32.1 g of S > 87.9 g of FeS 
Mole to mole calculations: 
This is an example of how to do mole to mole type problems:
Two atoms of sulphur react with three molecules of oxygen to form two molecules of sulphur trioxide, which is an air pollutant. 2 S + 3 O_{2} > 2 SO_{3} 
How many moles of sulphur react in this way with 9 moles
of
O_{2}? Solution: From the balanced equation you can see that 2 S react with 3 O_{2} Set up your ratio like this: 2 S = 3 O_{2} x 9 moles Cross multiply to get 2 * 9 moles = 3 * x
x = (2 * 9 moles) / 3 = 6 moles 
Therefore if 9 moles of oxygen are reacted then 6 moles of
S
must also be present. Note that the unit "moles" was carried through the calculation. 
Mole to Mole Calculations Worksheet 
The following files are recommended reading. Not
mandatory,
but highly recommended. 
Eggsamples of Concrete Stoichiometry 
Bridging the Stoichiometry Gap 