I would like to add a page to my website with a layout with animated panels that auto-slide around based on which one is clicked, as in Stackexchange’s Sites page:
https://stackexchange.com/sites
What language and what specific methodology did the designers of Stackexchange use for laying out that page, or more meaningfully, what language and methodology would you recommend I research, in order to learn to create something similar? Perhaps there is a tutorial somewhere for creating something similar to it?
From looking at the sources of that page (achieved by activating the developer console in Chrome and looking at the scripts panel.) I can see they are making use of the Isotope layout engine.
Isotope is a jQuery plugin written in JavaScript and the site linked above contains some solid documentation; however if you are new to JavaScript then they may be a little difficult to follow. A quick google brings up the following Isotope tutorial which may help you get started.