What is a buffer, and how does it respond to the addition of acid or alkali?

Firstly, I would try and establish with the tutee what a buffer is and define it. Going through the key aspects of what a buffer is. The standard definition I have for a buffer is 'A solution that minimises the change in pH upon addition of small amounts of alkali or acid'. Following that we would define a Bronsted Lowry acid and base to establish clarity in order to understand how it works. We would then go through the makeup of a buffer; a weak acid and its conjugate base pair and then determine the generic equilibrium equation HA <---> H+ + A-. Once this has been established then go onto trying to understand the buffers response to acid or alkali.

On the addition of acid, we would understand this is the addition of H+ ions and how the excess H+ reacts with the conjugate base to form HA and therefore reduce the acidity present, shifting the equilibrium to the left. On addition of alkali the OH- is increased and the so the dissociated H+ ions from the acid react with it to form water. This shifts the equilibrium to the right so more H+ ions are produced minimising the change in pH.