How can you change the proportions of reactants and products at equilibrium if Le Chatelier's principle is occurring?
The Henderson Hasselbalc equation is a good way to calculate both the pH and the concentration of acid/conjugate base in an equilibrium solution. According to it:

pH = pKa + log([A-]/[HA])

Since you want to know when [A-] = [HA], you are looking for when the pH is equal to the pKa. This means that you will have equal concentrations of the acid/conjugate base whenever your pH is equal to your pKa, which you can find by monitoring the pH. While adding more conjugate base will shift the equilibrium towards acid formation, it will normally increase the acid concentration less than the amount of base that you added.