Stoichiometry is a quantitatve process. Given an initial mass or volume of reactant or product, the molar relationships between reactants and products in a chemical reaction are used to calculate a specific mass or volume of another reactant or product.

Problems - Mass/Mass

Essentially, all stoichiometry problems can be broken down into three steps:
1. Take the given quantity (i.e. mass. volume) and convert to moles
2. Use a mole to mole ratio to find the number of moles of the desired compound
3. Answer the question - convert the moles of the desired compound to the appropriate quantity (i.e. mass, volume)

Consider the following reaction and problem:

Determine the mass of iron that is produced from 25.36 g of iron(III) oxide.
This problem is often referred to as a mass-mass problem since you are given the mass of a compound in the problem and asked to find the mass of another compound. The three step method described above can be applied in the setup shown below:

In the first conversion factor above, the molar mass of Fe2O3 is determined since it is needed to convert to moles (step one). When given a mass (as in this problem), dividing by molar mass always converts to moles. In the second conversion factor (step two), a ratio of Fe to Fe2O3 is determined from the coefficients in the reaction. It is worth noting that this is the only time the coefficients of the reaction are used when solving a stoichiometry problem. Finally, the molar mass of Fe is used to convert moles of Fe to grams of Fe (step three). It's worth noting that in a mass-mass problem, the first and third steps are opposites of each other. That is, in step one you convert grams to moles (divide by molar mass) and in the third step you convert moles to grams (multiply by molar mass). Alternatively, this may visually represented in a simplified manner:
25.36 g Fe2O3 ÷ 159.70 g/mol Fe2O3 × 2 Fe:1 Fe2O3 × 55.85 g/mol Fe = 17.74 g Fe

Problems - Mass/Volume

The next problem is a mass-volume problem. In this case, either the mass of a compound will be given and the volume of another is asked, or the volume of a gas will be given and the mass of another compound will be asked. Reconsider the equation from above:

Determine the volume of carbon dioxide gas that will be produced from 112.5 grams of iron at STP.
First, it's important to understand the concept of STP, standard temperature and pressure. Standard temperature and pressure is a set of conditions (273.15 K and 1 atm) at which 1 mole of any ideal gas will occupy 22.414 L. As a conversion factor, 1 mole gas = 22.414 L.
Although many authors will assume STP unless otherwise specified, it is important to determine the conditions of the reaction. If the reaction is not occuring at STP, the conversion factor given above cannot be used. The problem can still be solved, but the ideal gas law must be incorporated. Note the usage of the aforementioned conversion factor in the solution:

Problems - Volume/Volume

A volume-volume problem concerns only the gaseous compounds of a reaction. Again, the relationship between 1 mole of gas at STP and the molar volume of 22.414 L is important. Consider the reaction below:

What is the volume of ammonia gas will react with 22.5 L of oxygen gas?
Note that the first and last step in a volume-volume problem will cancel each other. This is because the first step, converting to liters of oxygen to moles, requires a division by 22.414. In the third step, conversion of moles of ammonia to liters, requires multiplication by 22.414. These two steps cancel each other and render step two (mole to mole ratio) the only important step. It needs to be stressed that this only happens in a volume-volume problem.

Problems - Limiting Reactant

In the previous example, it was assumed that there was an unlimited supply of carbon monoxide to react with all of the iron. Sometimes this is not an appropriate or plausible assumption. Sometimes two distinct masses of reactants are given, and it cannot be assumed that they will consume each other completely. Imagine trying to bake a cake. The recipe states that two eggs are needed to make a cake. With a dozen eggs available, six cakes can be made. What if the recipe also states that a cup of sugar is necessary and only four cups of sugar are available? Regardless of the dozen eggs, only four cakes can be made, because after consuming four cups of sugar (with eight eggs), there will be no sugar remaining. At this point, no more cakes can be made. Sugar is considered the limiting reactant in this example. The eggs are the excess reactant. Recall the reaction from before:

What mass of iron will be produced from 25.00 g of iron(III) oxide and 25.00 g of carbon monoxide?
The solution is similar to the mass-mass problem from before, except there are two problems being solved at the same time.

The reactant that produces the smaller mass (or volume for a gas) of product is the limiting reactant. The limiting reactant always dictates the mass/volume of product that is produced, therefore the smaller quantity of product is always the solution to a limiting reactant problem.