Calculate the number of moles that were required to neutralize the vinegar

Vinegar is diluted acetic acid. Most vinegar comes around <5% concentration.

Keeping this in mind, if you know the total volume of your vinegar and you know the molarity (mol/L) you can multiply volume x molarity to obtain the total amount of moles of acetic acid. 

Because acetic acid is a weak acid, the formula for the dissolving of acetic acid in water is CH3COOH + H2O <-> H3O(1+) + CH3COO(1-).

This shows that you have (about) 1 mole of H+ ions for each mole of acetic acid dissolved in solution.

Using the moles of H+ you can find out the amount of base you need using a stoichiometric ratio. 
For example, if you had exactly 2 moles of acetic acid in solution, you would need 2 moles of sodium hydroxide (NaOH) to neutralize it.

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