Difference between left and right derivatives?

Hello,

Would someone be able to provide me with an example to clarify the definitions of $\displaystyle \mathop {\lim }\limits_{x \to {x_0} + } f\left( x \right)$ and $\displaystyle \mathop {\lim }\limits_{x \to {x_0} - } f\left( x \right)$? I believe that I understand the calculus theorems, but not this (seemingly basic) idea of left and right limits. Both that, and I can never remember which way round their definitions are!

Sorry, I should have posted this in the analysis section. If someone could move it there, that would be great. :)