Mastering Buffer Solution Problems for Understanding pH Changes

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I have a somewhat decent understanding of what a buffer is (stops an acid/base from changing the pH so dramatically), but when it comes to problems involving them, I am flat out lost and I haven't been so frustrated before. What is there to know about these types of questions, like what will the pH be if you add xx mL of whatever to a buffer solution?
 

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The simplest (and in most cases good enough) approach is to just assume reaction (be it neutralization of the acid or protonation of the conjugate base) proceeded to the end, calculate new concentrations of the acid and its conjugate base, and plug both values into Henderson-Hasselbalch equation.

Actually you don't have to calculate concentrations, just numbers of moles. But as long as you don't feel confident, it is better to follow the well beaten path.