These are three awesome short videos (3 - 4 minutes each), that explain the quick-sort algorithm really well.
This video focuses purely on the algorithm and doesn't get distracted by implementation details, which is great if you're trying to understand the algorithm for the first time.
This video goes into some of the implementation details of quick-sort. Specifically, how to maintain a couple of pointers so that you can do in-place sorting (that is, not copy the entire array).
A bonus! An animated race between bubble-sort and quick-sort.
A pseudo-code implementation can be found on Wikipedia.
If you get stuck, feel free to shoot us your questions.
P.S.: See discussion posts for intuition on the algorithm, links to text tutorial and more information.